L'Essentiel à Retenir

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    Un peu de Théorie

    Fonction Racine f(x) = MMF.7h]Z3`00QEO=L]]637h2_h))m0b]FN`?^La=EQUGDh_bB8cCPbi(b[ZJfU9:bfdBSmnm`799PPZYF9J=3l1RlF6a4;EMI)mGjnD|GjbbRmN;kGbMc_;E)UPFaknFaL?^lnB^[9h?nn9alW6gWoa[Ye9NGVccAGjK1^To;lEaMmQO0J[^doD6P`*VW4CQA:3VUeVN1R32RMCh5X1Z|)o0_=(J[NW_MkNcAAILG[aMK3MYWRnb6lYP|lUVbcChl5aFTdei?)kf3nSmO0a4^5c)bogaYOZFUOoEFj0JQ]GbA2e[]N[DZlLoKZZbo;^ejB6K3fM)`T6]SXHgSl=lme*nCe0gFAnNRWe[|N7ll5;]T1_gCdKmHHce26dHh*gWR((iiS127DJh`cQi66H?hoCU:Gfo^A`kmA7jlQamNHjn7:4_AnS;LOYbV;hLYjm6CUn=d5NWm9gn)ehM6H:|I*PQ=5j?fU2IFUHXPoI08hRmTb63m8J835j)FBA;CY472*;[IFaP2)_EG`:BABeB6^1UbE`X3C)e=J0d`1](^o(GUdFSSi6KV2Z?[4?B[doH9RhAd`1PVDRZSYMYNjdlL5FHn|Q02CAba0=C7D0eR2XA=B3Y9BL59leBT5B1Y06:|I)l1=:`9C`56GNiBM_OTmM0l**D|88XM`H=D)d18]3lM4`_^8ZjOEG(R2_;HbL(J9j2YQB|3j0UXjXEMm(Le2WXaY5B^6Z=_Q^Jo[6(R4hH4B=hJo4d3:GQea]n54ICWcC]H=beJ5RIR?N0XBbTUbfCTjkC8|5TePZAk4XJlB94K_|6V2iZ5;58M0RZbB)bSW63TVjGV5n6V3M2c?J?JGmo6F;]:Q]kI?PB8]o|6K=FS6UokFGGQciUBm|[7l_bkFgMQ`eBg(*KdMIMd:2XXfHYPJ]f7UQVBK[D4|5TE_i4|QdCeEDfdJbm4l()9XWhTYQeC68iB=P=0b5j|dE07l[Nh59|lPS=PNT)24A_:8VhQb`_5`SFR02RIn^=AW23ZCDYEm[FF5o;5QZn()8P3WD7Z2QGKLQNEMb0K4lOg8RD3I0L^9_A05hB=b=URoSIP1^C]TF|=D2bb`6:Odji(MT)653|OP0)B]4i^_i|(_BCd[B^_M=a`k8]Y9^F7FY;LS)k`hm(4KZd*hGoJeC_BEI`Z6o5UkNj;W9foQnlEN4ZjoGFokE^lY5EHdCU;HjU`lYKSM?ll?;Fb6DaUUGLFV=WSG]FNgI]L[hJ?bTFd94(I[eN[O90C?4nRFV4Kb01V`aEkW?QjLnC[ane3PIdl|N7bMZP1Y`7WSa[0ceecZ[Zh?gXHO=j]bnZKcF)4FOU*g4|Jf`A[l]7mff|eRBX^BnZGO7Y|I*nFj:*7SmkA(VWGhmEhK5T:mikWA[*j*6M)M4ESlR07R?`AU_gRio(7Z0|W)b*XYHZZYjk9[Dk6e9XkjTY23[?KmMh6=VQN|8_YGWimNSk|gk1E;P)Wjm^EjMnN9[^Id30IKSXnSLG7:G=QfE0IE]TND3Q=[n^?Uk?=RTIgbQjUZMIC]mG[eng)AECG;jB?0odiM_f7_gNg]3cOeEd0IX.mmf

    Qu’est-ce donc que cette forme géométrique ?

    Le ∎ sous la racine représente un terme plus ou moins complexe qui dépend bien évidemment de x.

    Pour f(x) = (x+4)(x²-2) MMF.7h]Z3`00QEO=L]]637h2_h))m0b]FN`?^La=EQUGDh_bB8cCPbi(b[ZJfU9:bfdBSmnm`799PPZYF9J=3l1RlF6a4;EMI)mGjnD|GjbbRmN;kGbMc_;E)UPFaknFaL?^lnB^[9h?nn9alW6gWoa[Ye9NGVccAGjK1^To;lEaMmQO0J[^doD6P`*VW4CQA:3VUeVN1R32RMCh5X1Z|)o0_=(J[NW_MkNcAAILG[aMK3MYWRnb6lYP|lUVbcChl5aFTdei?)kf3nSmO0a4^5c)bogaYOZFUOoEFj0JQ]GbA2e[]N[DZlLoKZZbo;^ejB6K3fM)`T6]SXHgSl=lme*nCe0gFAnNRWe[|N7ll5;]T1_gCdKmHHce26dHh*gWR((iiS127DJh`cQi66H?hoCU:Gfo^A`kmA7jlQamNHjn7:4_AnS;LOYbV;hLYjm6CUn=d5NWm9gn)ehM6H:|I*PQ=5j?fU2IFUHXPoI08hRmTb63m8J835j)FBA;CY472*;[IFaP2)_EG`:BABeB6^1UbE`X3C)e=J0d`1](^o(GUdFSSi6KV2Z?[4?B[doH9RhAd`1PVDRZSYMYNjdlL5FHn|Q02CAba0=C7D0eR2XA=B3Y9BL59leBT5B1Y06:|I)l1=:`9C`56GNiBM_OTmM0l**D|88XM`H=D)d18]3lM4`_^8ZjOEG(R2_;HbL(J9j2YQB|3j0UXjXEMm(Le2WXaY5B^6Z=_Q^Jo[6(R4hH4B=hJo4d3:GQea]n54ICWcC]H=beJ5RIR?N0XBbTUbfCTjkC8|5TePZAk4XJlB94K_|6V2iZ5;58M0RZbB)bSW63TVjGV5n6V3M2c?J?JGmo6F;]:Q]kI?PB8]o|6K=FS6UokFGGQciUBm|[7l_bkFgMQ`eBg(*KdMIMd:2XXfHYPJ]f7UQVBK[D4|5TE_i4|QdCeEDfdJbm4l()9XWhTYQeC68iB=P=0b5j|dE07l[Nh59|lPS=PNT)24A_:8VhQb`_5`SFR02RIn^=AW23ZCDYEm[FF5o;5QZn()8P3WD7Z2QGKLQNEMb0K4lOg8RD3I0L^9_A05hB=b=URoSIP1^C]TF|=D2bb`6:Odji(MT)653|OP0)B]4i^_i|(_BCd[B^_M=a`k8]Y9^F7FY;LS)k`hm(4KZd*hGoJeC_BEI`Z6o5UkNj;W9foQnlEN4ZjoGFokE^lY5EHdCU;HjU`lYKSM?ll?;Fb6DaUUGLFV=WSG]FNgI]L[hJ?bTFd94(I[eN[O90C?4nRFV4Kb01V`aEkW?QjLnC[ane3PIdl|N7bMZP1Y`7WSa[0ceecZ[Zh?gXHO=j]bnZKcF)4FOU*g4|Jf`A[l]7mff|eRBX^BnZGO7Y|I*nFj:*7SmkA(VWGhmEhK5T:mikWA[*j*6M)M4ESlR07R?`AU_gRio(7Z0|W)b*XYHZZYjk9[Dk6e9XkjTY23[?KmMh6=VQN|8_YGWimNSk|gk1E;P)Wjm^EjMnN9[^Id30IKSXnSLG7:G=QfE0IE]TND3Q=[n^?Uk?=RTIgbQjUZMIC]mG[eng)AECG;jB?0odiM_f7_gNg]3cOeEd0IX.mmf , nous avons ∎ = ( x + 4 )( x² - 2 )

    Quelle contrainte impose la fonction ?

    Tout ce qui se trouve sous une racine carrée doit être positif ou nul, ainsi nous avons forcément ∎ ≥ 0. Nous obtenons alors le domaine de définition en résolvant cette inéquation grâce à un tableau de signes.

    Exemple : f(x) = x² - 4 MMF.7h]Z3`00QEO=L]]637h2_h))m0b]FN`?^La=EQUGDh_bB8cCPbi(b[ZJfU9:bfdBSmnm`799PPZYF9J=3l1RlF6a4;EMI)mGjnD|GjbbRmN;kGbMc_;E)UPFaknFaL?^lnB^[9h?nn9alW6gWoa[Ye9NGVccAGjK1^To;lEaMmQO0J[^doD6P`*VW4CQA:3VUeVN1R32RMCh5X1Z|)o0_=(J[NW_MkNcAAILG[aMK3MYWRnb6lYP|lUVbcChl5aFTdei?)kf3nSmO0a4^5c)bogaYOZFUOoEFj0JQ]GbA2e[]N[DZlLoKZZbo;^ejB6K3fM)`T6]SXHgSl=lme*nCe0gFAnNRWe[|N7ll5;]T1_gCdKmHHce26dHh*gWR((iiS127DJh`cQi66H?hoCU:Gfo^A`kmA7jlQamNHjn7:4_AnS;LOYbV;hLYjm6CUn=d5NWm9gn)ehM6H:|I*PQ=5j?fU2IFUHXPoI08hRmTb63m8J835j)FBA;CY472*;[IFaP2)_EG`:BABeB6^1UbE`X3C)e=J0d`1](^o(GUdFSSi6KV2Z?[4?B[doH9RhAd`1PVDRZSYMYNjdlL5FHn|Q02CAba0=C7D0eR2XA=B3Y9BL59leBT5B1Y06:|I)l1=:`9C`56GNiBM_OTmM0l**D|88XM`H=D)d18]3lM4`_^8ZjOEG(R2_;HbL(J9j2YQB|3j0UXjXEMm(Le2WXaY5B^6Z=_Q^Jo[6(R4hH4B=hJo4d3:GQea]n54ICWcC]H=beJ5RIR?N0XBbTUbfCTjkC8|5TePZAk4XJlB94K_|6V2iZ5;58M0RZbB)bSW63TVjGV5n6V3M2c?J?JGmo6F;]:Q]kI?PB8]o|6K=FS6UokFGGQciUBm|[7l_bkFgMQ`eBg(*KdMIMd:2XXfHYPJ]f7UQVBK[D4|5TE_i4|QdCeEDfdJbm4l()9XWhTYQeC68iB=P=0b5j|dE07l[Nh59|lPS=PNT)24A_:8VhQb`_5`SFR02RIn^=AW23ZCDYEm[FF5o;5QZn()8P3WD7Z2QGKLQNEMb0K4lOg8RD3I0L^9_A05hB=b=URoSIP1^C]TF|=D2bb`6:Odji(MT)653|OP0)B]4i^_i|(_BCd[B^_M=a`k8]Y9^F7FY;LS)k`hm(4KZd*hGoJeC_BEI`Z6o5UkNj;W9foQnlEN4ZjoGFokE^lY5EHdCU;HjU`lYKSM?ll?;Fb6DaUUGLFV=WSG]FNgI]L[hJ?bTFd94(I[eN[O90C?4nRFV4Kb01V`aEkW?QjLnC[ane3PIdl|N7bMZP1Y`7WSa[0ceecZ[Zh?gXHO=j]bnZKcF)4FOU*g4|Jf`A[l]7mff|eRBX^BnZGO7Y|I*nFj:*7SmkA(VWGhmEhK5T:mikWA[*j*6M)M4ESlR07R?`AU_gRio(7Z0|W)b*XYHZZYjk9[Dk6e9XkjTY23[?KmMh6=VQN|8_YGWimNSk|gk1E;P)Wjm^EjMnN9[^Id30IKSXnSLG7:G=QfE0IE]TND3Q=[n^?Uk?=RTIgbQjUZMIC]mG[eng)AECG;jB?0odiM_f7_gNg]3cOeEd0IX.mmf

    Ici, ∎ = x² - 4 . Ainsi on résout x² - 4 ≥ 0. Ce polynôme du second degré est du signe de a = 1 positif, sauf entre ses racines -2 et 2. On obtient donc que x² - 4 ≥ 0 quand x ∈ ; 2 MMF.7h_N3`00QEMOLn963?l4n*hlVQV7FNdONgem8]BG(PdV0kiL7gQa[fk:=86[`kEgcNBkEeZ_KIVcJDR2OY9FdTn[GLa^VKeOKeKcO;W)[Uj_MX]=)|oGVf1EW?iH5HokCi?k|WXi7XZWbLOmHO:gWDTi_M[Ubo`^3M:o_QBWoO5`3JQjB3MK31:HL1:54h6J7nMi6P244jW`C`2Z8GjWTWMBXcGmiOi^_|b2jMGKeFjKi_Tb^jD:]]]|_TZ33bmU=MVFYm?nl8SN;jM0Q:_EXSbL_UCO|_:O)PFZHEP]cmBbEZ])_GkjkKHZbcmKVajbnG3V;1cDjVPhNAcVnnObIH:jbNKhG1aJR`dGaboE7[UaofCD7lIHSm264Mi`RCQLHPhSe664)hbCQf7f(4iOW]?gbNGH[Xo*UiOXbd_di*Qm)D9OS])G`oCU)7de|_]ZQ;hjYnodon;ATB78FXH**^?eZ0fEZFF5(VP?=8;H)aTbB6n8b)3UV4Fbi1AiT22`G|H1Q[1NoCTPFM*RU*5NU|b5bS0cF`(Z0kc1]9To^bXJOHcLa4aiI1fBOWg2T[Q2C0)0EB:Y)ejVm5Yih;X`li612VSTR0NV?X1Z47DRJT3B:dh:CYZE8:T3B*(DHbMi2jAQBgP9(^iZTkJOToM0l*8D|8HX]`L=D)d68]1lMd`_^8Zj_2YVa9GU|A(6=2m1D`WF1m2BDMF:^fT)jQ9dhdPUG;M6?`g=o5Q6A2N(R15l]7PIQ|[`j`gO2Z=YCYYa()iH=:a(a6O0D1GBbiK9BCMYTF0b6hE8MRf=N1(RUkh1YX|JAB`BKH9ZjXR|HmbPY(|Bll(*ld68FOjHl__346_GfMPS`iL*nBIWc4HaY_cJbfh)OLVFdR|Obo;d]Yk31RU^hX=XjbUXD=AA|eC0MG|OF6I9^]8B`FCFoTBbS8WZ)Y]X=]j9HA^CA7a9c2HV|A`Tk8B14;fkAD0Ob]k5YMS=8c*7Y]|P4;e;BL*mI7Vk*;11110mFnmZ17La]BKUF]|Jjf?I*|(GAQc4XNh0=NFj3MW[R[|Pfmd7MdG:1TP)g(UX06n9^b=URoSNP;|VKH_HJ81TQ`(DoiabefAk`H1Ri`?`XQBMXi_?YT9oDi[F]KLkk[9|6nU^b`je;KVMgn=7YPQMfJ72ma[E)LT:3_F]n?9F=dG)c]o1FaF^|Ui_oGo[KSjbJXbX_(FaM5QiZg6JkekN6[TZaZZ:Ff_|[77?JRn^CBighgnJ1K*UPeE_e^|l43(lCf8FhAn*P4)6:_Nil?ckfMN?FPL3)_Wm`fA]D0?)0dnN]H6N)^MEMOAnm;1i|clDeKLJahRcl[4hUCFfR3OUTo|fEV|Be3`DeKkhmJVD_UZRT9hnNDC5Yem?EN6aI2_NNidJd)T1WCWC5Do8P1hSl4AKmh^Oc1jP;9c|T::A:ZZN^bJefa]BJ)nY:*Pj;nhf^1WI|G[6;jEinOGTik=n`Dbh2En|kmKWO[RKkVM0`6Fhj)IW5abUkHME*6eKIWU0hKHo[CoNc;LY6MlXNYJWFDkOEfmNMgU07lJ_:;k]7X9Xn[KKhW(GC)U=a]?M8_QQbY`Jj`8cM0|0bJ4C=4iTgFgaZ3TOn^o2K?51bkJA)go_m8KEo*LMF:Dk.mmf 2 ; + MMF.7h_N3`00QEMOLn963?l4n*hlVQV7FNdONgem8]BG(PdV0kiL7gQa[fk:=86[`kEgcNBkEeZ_KIVcJDR2OY9FdTn[GLa^VKeOKeKcO;W)[Uj_MX]=)|oGVf1EW?iH5HokCi?k|WXi7XZWbLOmHO:gWDTi_M[Ubo`^3M:o_QBWoO5`3JQjB3MK31:HL1:54h6J7nMi6P244jW`C`2Z8GjWTWMBXcGmiOi^_|b2jMGKeFjKi_Tb^jD:]]]|_TZ33bmU=MVFYm?nl8SN;jM0Q:_EXSbL_UCO|_:O)PFZHEP]cmBbEZ])_GkjkKHZbcmKVajbnG3V;1cDjVPhNAcVnnObIH:jbNKhG1aJR`dGaboE7[UaofCD7lIHSm264Mi`RCQLHPhSe664)hbCQf7f(4iOW]?gbNGH[Xo*UiOXbd_di*Qm)D9OS])G`oCU)7de|_]ZQ;hjYnodon;ATB78FXH**^?eZ0fEZFF5(VP?=8;H)aTbB6n8b)3UV4Fbi1AiT22`G|H1Q[1NoCTPFM*RU*5NU|b5bS0cF`(Z0kc1]9To^bXJOHcLa4aiI1fBOWg2T[Q2C0)0EB:Y)ejVm5Yih;X`li612VSTR0NV?X1Z47DRJT3B:dh:CYZE8:T3B*(DHbMi2jAQBgP9(^iZTkJOToM0l*8D|8HX]`L=D)d68]1lMd`_^8Zj_2YVa9GU|A(6=2m1D`WF1m2BDMF:^fT)jQ9dhdPUG;M6?`g=o5Q6A2N(R15l]7PIQ|[`j`gO2Z=YCYYa()iH=:a(a6O0D1GBbiK9BCMYTF0b6hE8MRf=N1(RUkh1YX|JAB`BKH9ZjXR|HmbPY(|Bll(*ld68FOjHl__346_GfMPS`iL*nBIWc4HaY_cJbfh)OLVFdR|Obo;d]Yk31RU^hX=XjbUXD=AA|eC0MG|OF6I9^]8B`FCFoTBbS8WZ)Y]X=]j9HA^CA7a9c2HV|A`Tk8B14;fkAD0Ob]k5YMS=8c*7Y]|P4;e;BL*mI7Vk*;11110mFnmZ17La]BKUF]|Jjf?I*|(GAQc4XNh0=NFj3MW[R[|Pfmd7MdG:1TP)g(UX06n9^b=URoSNP;|VKH_HJ81TQ`(DoiabefAk`H1Ri`?`XQBMXi_?YT9oDi[F]KLkk[9|6nU^b`je;KVMgn=7YPQMfJ72ma[E)LT:3_F]n?9F=dG)c]o1FaF^|Ui_oGo[KSjbJXbX_(FaM5QiZg6JkekN6[TZaZZ:Ff_|[77?JRn^CBighgnJ1K*UPeE_e^|l43(lCf8FhAn*P4)6:_Nil?ckfMN?FPL3)_Wm`fA]D0?)0dnN]H6N)^MEMOAnm;1i|clDeKLJahRcl[4hUCFfR3OUTo|fEV|Be3`DeKkhmJVD_UZRT9hnNDC5Yem?EN6aI2_NNidJd)T1WCWC5Do8P1hSl4AKmh^Oc1jP;9c|T::A:ZZN^bJefa]BJ)nY:*Pj;nhf^1WI|G[6;jEinOGTik=n`Dbh2En|kmKWO[RKkVM0`6Fhj)IW5abUkHME*6eKIWU0hKHo[CoNc;LY6MlXNYJWFDkOEfmNMgU07lJ_:;k]7X9Xn[KKhW(GC)U=a]?M8_QQbY`Jj`8cM0|0bJ4C=4iTgFgaZ3TOn^o2K?51bkJA)go_m8KEo*LMF:Dk.mmf . Ainsi Df = ; 2 MMF.7h_N3`00QEMOLn963?l4n*hlVQV7FNdONgem8]BG(PdV0kiL7gQa[fk:=86[`kEgcNBkEeZ_KIVcJDR2OY9FdTn[GLa^VKeOKeKcO;W)[Uj_MX]=)|oGVf1EW?iH5HokCi?k|WXi7XZWbLOmHO:gWDTi_M[Ubo`^3M:o_QBWoO5`3JQjB3MK31:HL1:54h6J7nMi6P244jW`C`2Z8GjWTWMBXcGmiOi^_|b2jMGKeFjKi_Tb^jD:]]]|_TZ33bmU=MVFYm?nl8SN;jM0Q:_EXSbL_UCO|_:O)PFZHEP]cmBbEZ])_GkjkKHZbcmKVajbnG3V;1cDjVPhNAcVnnObIH:jbNKhG1aJR`dGaboE7[UaofCD7lIHSm264Mi`RCQLHPhSe664)hbCQf7f(4iOW]?gbNGH[Xo*UiOXbd_di*Qm)D9OS])G`oCU)7de|_]ZQ;hjYnodon;ATB78FXH**^?eZ0fEZFF5(VP?=8;H)aTbB6n8b)3UV4Fbi1AiT22`G|H1Q[1NoCTPFM*RU*5NU|b5bS0cF`(Z0kc1]9To^bXJOHcLa4aiI1fBOWg2T[Q2C0)0EB:Y)ejVm5Yih;X`li612VSTR0NV?X1Z47DRJT3B:dh:CYZE8:T3B*(DHbMi2jAQBgP9(^iZTkJOToM0l*8D|8HX]`L=D)d68]1lMd`_^8Zj_2YVa9GU|A(6=2m1D`WF1m2BDMF:^fT)jQ9dhdPUG;M6?`g=o5Q6A2N(R15l]7PIQ|[`j`gO2Z=YCYYa()iH=:a(a6O0D1GBbiK9BCMYTF0b6hE8MRf=N1(RUkh1YX|JAB`BKH9ZjXR|HmbPY(|Bll(*ld68FOjHl__346_GfMPS`iL*nBIWc4HaY_cJbfh)OLVFdR|Obo;d]Yk31RU^hX=XjbUXD=AA|eC0MG|OF6I9^]8B`FCFoTBbS8WZ)Y]X=]j9HA^CA7a9c2HV|A`Tk8B14;fkAD0Ob]k5YMS=8c*7Y]|P4;e;BL*mI7Vk*;11110mFnmZ17La]BKUF]|Jjf?I*|(GAQc4XNh0=NFj3MW[R[|Pfmd7MdG:1TP)g(UX06n9^b=URoSNP;|VKH_HJ81TQ`(DoiabefAk`H1Ri`?`XQBMXi_?YT9oDi[F]KLkk[9|6nU^b`je;KVMgn=7YPQMfJ72ma[E)LT:3_F]n?9F=dG)c]o1FaF^|Ui_oGo[KSjbJXbX_(FaM5QiZg6JkekN6[TZaZZ:Ff_|[77?JRn^CBighgnJ1K*UPeE_e^|l43(lCf8FhAn*P4)6:_Nil?ckfMN?FPL3)_Wm`fA]D0?)0dnN]H6N)^MEMOAnm;1i|clDeKLJahRcl[4hUCFfR3OUTo|fEV|Be3`DeKkhmJVD_UZRT9hnNDC5Yem?EN6aI2_NNidJd)T1WCWC5Do8P1hSl4AKmh^Oc1jP;9c|T::A:ZZN^bJefa]BJ)nY:*Pj;nhf^1WI|G[6;jEinOGTik=n`Dbh2En|kmKWO[RKkVM0`6Fhj)IW5abUkHME*6eKIWU0hKHo[CoNc;LY6MlXNYJWFDkOEfmNMgU07lJ_:;k]7X9Xn[KKhW(GC)U=a]?M8_QQbY`Jj`8cM0|0bJ4C=4iTgFgaZ3TOn^o2K?51bkJA)go_m8KEo*LMF:Dk.mmf 2 ; + MMF.7h_N3`00QEMOLn963?l4n*hlVQV7FNdONgem8]BG(PdV0kiL7gQa[fk:=86[`kEgcNBkEeZ_KIVcJDR2OY9FdTn[GLa^VKeOKeKcO;W)[Uj_MX]=)|oGVf1EW?iH5HokCi?k|WXi7XZWbLOmHO:gWDTi_M[Ubo`^3M:o_QBWoO5`3JQjB3MK31:HL1:54h6J7nMi6P244jW`C`2Z8GjWTWMBXcGmiOi^_|b2jMGKeFjKi_Tb^jD:]]]|_TZ33bmU=MVFYm?nl8SN;jM0Q:_EXSbL_UCO|_:O)PFZHEP]cmBbEZ])_GkjkKHZbcmKVajbnG3V;1cDjVPhNAcVnnObIH:jbNKhG1aJR`dGaboE7[UaofCD7lIHSm264Mi`RCQLHPhSe664)hbCQf7f(4iOW]?gbNGH[Xo*UiOXbd_di*Qm)D9OS])G`oCU)7de|_]ZQ;hjYnodon;ATB78FXH**^?eZ0fEZFF5(VP?=8;H)aTbB6n8b)3UV4Fbi1AiT22`G|H1Q[1NoCTPFM*RU*5NU|b5bS0cF`(Z0kc1]9To^bXJOHcLa4aiI1fBOWg2T[Q2C0)0EB:Y)ejVm5Yih;X`li612VSTR0NV?X1Z47DRJT3B:dh:CYZE8:T3B*(DHbMi2jAQBgP9(^iZTkJOToM0l*8D|8HX]`L=D)d68]1lMd`_^8Zj_2YVa9GU|A(6=2m1D`WF1m2BDMF:^fT)jQ9dhdPUG;M6?`g=o5Q6A2N(R15l]7PIQ|[`j`gO2Z=YCYYa()iH=:a(a6O0D1GBbiK9BCMYTF0b6hE8MRf=N1(RUkh1YX|JAB`BKH9ZjXR|HmbPY(|Bll(*ld68FOjHl__346_GfMPS`iL*nBIWc4HaY_cJbfh)OLVFdR|Obo;d]Yk31RU^hX=XjbUXD=AA|eC0MG|OF6I9^]8B`FCFoTBbS8WZ)Y]X=]j9HA^CA7a9c2HV|A`Tk8B14;fkAD0Ob]k5YMS=8c*7Y]|P4;e;BL*mI7Vk*;11110mFnmZ17La]BKUF]|Jjf?I*|(GAQc4XNh0=NFj3MW[R[|Pfmd7MdG:1TP)g(UX06n9^b=URoSNP;|VKH_HJ81TQ`(DoiabefAk`H1Ri`?`XQBMXi_?YT9oDi[F]KLkk[9|6nU^b`je;KVMgn=7YPQMfJ72ma[E)LT:3_F]n?9F=dG)c]o1FaF^|Ui_oGo[KSjbJXbX_(FaM5QiZg6JkekN6[TZaZZ:Ff_|[77?JRn^CBighgnJ1K*UPeE_e^|l43(lCf8FhAn*P4)6:_Nil?ckfMN?FPL3)_Wm`fA]D0?)0dnN]H6N)^MEMOAnm;1i|clDeKLJahRcl[4hUCFfR3OUTo|fEV|Be3`DeKkhmJVD_UZRT9hnNDC5Yem?EN6aI2_NNidJd)T1WCWC5Do8P1hSl4AKmh^Oc1jP;9c|T::A:ZZN^bJefa]BJ)nY:*Pj;nhf^1WI|G[6;jEinOGTik=n`Dbh2En|kmKWO[RKkVM0`6Fhj)IW5abUkHME*6eKIWU0hKHo[CoNc;LY6MlXNYJWFDkOEfmNMgU07lJ_:;k]7X9Xn[KKhW(GC)U=a]?M8_QQbY`Jj`8cM0|0bJ4C=4iTgFgaZ3TOn^o2K?51bkJA)go_m8KEo*LMF:Dk.mmf

     

    Fonction Inverse f(x) = 1 MMF.7h]`3`00QEO=L]]637h2_h))m0b]FN`?^La=EQUGDd_bB8cCPbm|b[ZJfU9::fdBSmnm`)jB11EB]F`;7k0;h(=R8NYQ|GZogRaWaF:m^WRmN9Q_lUVagTC;l_SW|WcLOI[LEOG;HElnCCk^mY=ok5C:bh^7HU7LiU7nmiOb^3_|[`1EmoUVRdhR4dnBN29*lm)|b2)0N6;SRAB0FPW_Y7ZWbISoNWLkFjbRbh^gRhM]GQB;e*dU|=f^I||ln_1BeI=]MCc^mXnhn^DHRGRiW5OkhiOjfj[jedM0=*b[iHUJN[GZe)^WgfoZZ_Z[]NTQFg1WC]b1EbO3`M)hf3eG;a?DCCJ7ig;OFV`l?gbYMlR=[lm6el(Hja7J((8KcQ67LlaQQ3Z(L8MalS3(7|KYbe?j8KPL)oDAn_8LOGV)_QbQ;dOXbg7jLYRn7:N_ATiOSM1GYoBMoS]N7AV3m3;449^PAff|S9LEbZ03d0SB|(R***I3*XHPYlbCYDE901T26fA|H8Smk|lAbL:;U0H4FK8UU8JIFPlX3*P6ddKnk;9Xm2Ub4e(ET7E8Q_dI2n8B(*d0UXVTjPBI`V|EP:_2=7P6BZ2A4njHjP2Z*EB9Y05I;cTY)6VFPZ*:I0e*S9gT9I26KN4Yb;C;CMYnC5h3aA=*`0ZRg1Td*;D7R43cdc4mib[YhZZD4ENFnlhHd3`5CBWHh41;AUD[_Tach5?*cD9:hJXeQViXn|Lb8SYSA8cP[LGC(9A6f6ohDAQ=OM:dPg7GXV5U4]h3Q[:**KI(c[Y)B`BCFB|T|R]Y`X^*^?0=(9gG966Nj11DTdMR7N(6IEfDU5n6U3M2b^:W53mLQUBkbZH16Kj5b3LaDmJ::LGG*GIm65:f55h5GiJ7]kh?6jBhRCNRmEg*X:BSIRV1ZgHNF6K9^]*b`FAFoTbbR9WZ:Y]Ye]jIH*NC9Ga;bSXV|aaTk8J14;gI8Z0?IFm`:CIiQ)K0M0L4XSNDA=Y3UYL;16]40=6cmDHS^(7DVY*[KF_dek:5QVm()4QSg*4ZbUG[|ULE=b3Kd`Lg8VD390O^ISB0UlC=B=TROSKPaZA]4F|=T)abP):ODfi(]P(65;|OP8=BM0]MOcHIQTUYfZFmdg73|RfTViHMJT]b(k_3Sd`A^kASQNlNnIQT1HOjEW`5Zn|RInO_4:`:MmVP]n6oMI)?[1XmZV1a;1eF`FZLiXMG|2H^Rk6|d]JJ)V_J|mZcNk?ceOROHP4MbF3FVoFjR(*Dki)H9_P7962CXLYm;ScoLO;e`n]P*2MoO9Sd1SF`N)39da_XZG=FehN`SQhf[gOk|_kVLHYhECfFalYSRgQC?KT_HejCXNJn[7OUKdnE3=TBQOch:B1:?_mj[(^09M_a?^SDP4h?j(b9[Wa21_*HPCOJ^UolI0h0IN5TQaBeE5WgUV]B^k(QQ*h[=CW1aO?K3Ak6jU0ohgOBX_Yj3?gYGc0E[|?Wjm_ejCXlCOLc8)0fg7CmRg))d_K3(Z:b;EI5A)jf?jloG|nf)AWOb?^Zb5L5OEnmOWdXX^CbUHAiY2kO_21A^(MW^L^g=mc`7k86FS`.mmf

    Qu’est-ce donc que cette forme géométrique ?

    Le ⨁ au dénominateur représente un terme plus ou moins complexe qui dépend bien évidemment de x.

    Pour f(x) = 1 x²(x-2) MMF.7h]`3`00QEO=L]]637h2_h))m0b]FN`?^La=EQUGDd_bB8cCPbm|b[ZJfU9::fdBSmnm`)jB11EB]F`;7k0;h(=R8NYQ|GZogRaWaF:m^WRmN9Q_lUVagTC;l_SW|WcLOI[LEOG;HElnCCk^mY=ok5C:bh^7HU7LiU7nmiOb^3_|[`1EmoUVRdhR4dnBN29*lm)|b2)0N6;SRAB0FPW_Y7ZWbISoNWLkFjbRbh^gRhM]GQB;e*dU|=f^I||ln_1BeI=]MCc^mXnhn^DHRGRiW5OkhiOjfj[jedM0=*b[iHUJN[GZe)^WgfoZZ_Z[]NTQFg1WC]b1EbO3`M)hf3eG;a?DCCJ7ig;OFV`l?gbYMlR=[lm6el(Hja7J((8KcQ67LlaQQ3Z(L8MalS3(7|KYbe?j8KPL)oDAn_8LOGV)_QbQ;dOXbg7jLYRn7:N_ATiOSM1GYoBMoS]N7AV3m3;449^PAff|S9LEbZ03d0SB|(R***I3*XHPYlbCYDE901T26fA|H8Smk|lAbL:;U0H4FK8UU8JIFPlX3*P6ddKnk;9Xm2Ub4e(ET7E8Q_dI2n8B(*d0UXVTjPBI`V|EP:_2=7P6BZ2A4njHjP2Z*EB9Y05I;cTY)6VFPZ*:I0e*S9gT9I26KN4Yb;C;CMYnC5h3aA=*`0ZRg1Td*;D7R43cdc4mib[YhZZD4ENFnlhHd3`5CBWHh41;AUD[_Tach5?*cD9:hJXeQViXn|Lb8SYSA8cP[LGC(9A6f6ohDAQ=OM:dPg7GXV5U4]h3Q[:**KI(c[Y)B`BCFB|T|R]Y`X^*^?0=(9gG966Nj11DTdMR7N(6IEfDU5n6U3M2b^:W53mLQUBkbZH16Kj5b3LaDmJ::LGG*GIm65:f55h5GiJ7]kh?6jBhRCNRmEg*X:BSIRV1ZgHNF6K9^]*b`FAFoTbbR9WZ:Y]Ye]jIH*NC9Ga;bSXV|aaTk8J14;gI8Z0?IFm`:CIiQ)K0M0L4XSNDA=Y3UYL;16]40=6cmDHS^(7DVY*[KF_dek:5QVm()4QSg*4ZbUG[|ULE=b3Kd`Lg8VD390O^ISB0UlC=B=TROSKPaZA]4F|=T)abP):ODfi(]P(65;|OP8=BM0]MOcHIQTUYfZFmdg73|RfTViHMJT]b(k_3Sd`A^kASQNlNnIQT1HOjEW`5Zn|RInO_4:`:MmVP]n6oMI)?[1XmZV1a;1eF`FZLiXMG|2H^Rk6|d]JJ)V_J|mZcNk?ceOROHP4MbF3FVoFjR(*Dki)H9_P7962CXLYm;ScoLO;e`n]P*2MoO9Sd1SF`N)39da_XZG=FehN`SQhf[gOk|_kVLHYhECfFalYSRgQC?KT_HejCXNJn[7OUKdnE3=TBQOch:B1:?_mj[(^09M_a?^SDP4h?j(b9[Wa21_*HPCOJ^UolI0h0IN5TQaBeE5WgUV]B^k(QQ*h[=CW1aO?K3Ak6jU0ohgOBX_Yj3?gYGc0E[|?Wjm_ejCXlCOLc8)0fg7CmRg))d_K3(Z:b;EI5A)jf?jloG|nf)AWOb?^Zb5L5OEnmOWdXX^CbUHAiY2kO_21A^(MW^L^g=mc`7k86FS`.mmf , nous avons ⨁ = x² ( x - 2 )

    Quelle contrainte impose la fonction ?

    Tout ce qui est au dénominateur ne doit jamais s'annuler, nous avons donc ⨁ ≠ 0. Nous obtenons alors le domaine de définition Df = MMF.7h]V3`00QEM]Lm|f3?h5oPonZ=`Y?X8_4]E_SZMV_|EbcUKKgLgkX6EZjY]ONXZj]N_U_hlP:*Ub9Bm)HS`02N01*ESN;K)gjleZWRoGfNCkI;OHY?=l_*UFAOeYECc_WjJ?IOEb?QF7jHOmJOZgWW5n(mWUbo`Q3CiFaE)m?imVWn[S`FSOYi^]lA)XL1Z5DfHd?lgc=008YcZLLPI6bn4=Smi`=:Jo?Sk(UeU`(gVMk;IYWRncNlaQ^lgVZcAhme9FdfeIeo_C|eWmDPL|G:dFiJWnDWg;bWmL1:)6HCFoD7)W5YejOOSc_R[;_eZK7;9iMn[27CQe=1`l3_?m|GbI6]edLchFYmJR`lGiBkDgg)SjI7*mS;4NX*dS_)4JLKS674JX``Qg62L?`naQW3joY)n3lk5C7j7?[m7WenSc4OYlQ3hOYln7jO=anV;Tm(D8OG59gn[o=EN7Ql2M3264b^^==QC:bL;883f*1|AnTD83mhH83Ej)RBN=Rb8?4P)dUdd3*nQfO`i*ITk4=(3;W2c1==A()h1YP3NX=_9WVdFSS`dg=Q(NJH^hgin*83HAe*0PVG2|SYLa_1*Nf2[(_6O011XiXXja3R0JQ9F86Y3dT^)(TRHYL:a0dP11f75J0Zk85YX2Sk_L^)k7Y3D*=041Y232WT43A7^01TQj)Z[WG4AMG14ChT9Cg`T1TZHP(*G]7DQ)Z4Y1UdT:G0ZbFHPYg;I6g`e=ofQ2A2J4R6:d]FPJ2]?`naDm2RFaCiYfD?IJ=:aDA7]0HAKLbi[8BMMY4B(bJHF8MbF=J14R6kh1Z_(JAL*C7X9XlXRdIMbPY8|Bdl|*ddJ8BO`Hho_;44]KfMPSAKLPnBIVC5Xaa_SBbkH?OLXJ``__Bm?`f_EQP`*edDKD[P|J57GD=2I`flh3CBa9Ue[2R4c:Wg0B(A5MIA=9fS]Ai62BR6j9BLLTVX:4g31P[3MK6?*Qk`d^*BH?TaBXkX20mHHBRg]8dg818hd8`7ZfgVP4)iQJTk2UKHg^F[I*dHdA1G4X)h15^FeMmZYR1fAknV1796l0Yl3NS0K*T]PIbE]4c`K|V=*]8Zd1W5`)4?AcbXk9M|208?L3c:1TgD;KWdf6OU:ZMVW_M)b`K0]YYfF7fY;Lcao=AbH;KMZQ()l)^IQX1H_jE_?bE]]5eTkO`E^5fJFmG__ofThn]4[SDGR;IFVal5IU=Cnl_3FbFHaU5KOFf5[SWUEOgI]L[lKo50_`B0JcgZcGNL1ViSjaFFCn00GCI4IU?aN)7bnnOSPM3)ShS`nCcR065PllNCX3?WG)Zn[|en73i]gnE5CO78h=c|[WXRhMePI_bT)1glNL9S6JmdFe;ohhU=aWRaCBn|TSC3kmFUN5aic|N)]eHT0W1gCZ*ULL30=lS30gF]]OllW|PI6IUBdBf595eE|^DFg?1QGB[iCXa2aN?6c(HFCWjVRnU^KUem[gYg_1S=T)Gj`OeYO[c6WJW`71K3)KkWjacXfdOKL:|6c;;0o*gOKWmHNknCI5hb]jco8dbo7kj]gggN:g((B(kLo_`NKVeJci3fXO=AD.mmf \ { solution(s) de ⨁ = 0 }

    Exemple : f(x) = 1 (x-1)(2x+4) MMF.7h]`3`00QEO=L]]637h2_h))m0b]FN`?^La=EQUGDd_bB8cCPbm|b[ZJfU9::fdBSmnm`)jB11EB]F`;7k0;h(=R8NYQ|GZogRaWaF:m^WRmN9Q_lUVagTC;l_SW|WcLOI[LEOG;HElnCCk^mY=ok5C:bh^7HU7LiU7nmiOb^3_|[`1EmoUVRdhR4dnBN29*lm)|b2)0N6;SRAB0FPW_Y7ZWbISoNWLkFjbRbh^gRhM]GQB;e*dU|=f^I||ln_1BeI=]MCc^mXnhn^DHRGRiW5OkhiOjfj[jedM0=*b[iHUJN[GZe)^WgfoZZ_Z[]NTQFg1WC]b1EbO3`M)hf3eG;a?DCCJ7ig;OFV`l?gbYMlR=[lm6el(Hja7J((8KcQ67LlaQQ3Z(L8MalS3(7|KYbe?j8KPL)oDAn_8LOGV)_QbQ;dOXbg7jLYRn7:N_ATiOSM1GYoBMoS]N7AV3m3;449^PAff|S9LEbZ03d0SB|(R***I3*XHPYlbCYDE901T26fA|H8Smk|lAbL:;U0H4FK8UU8JIFPlX3*P6ddKnk;9Xm2Ub4e(ET7E8Q_dI2n8B(*d0UXVTjPBI`V|EP:_2=7P6BZ2A4njHjP2Z*EB9Y05I;cTY)6VFPZ*:I0e*S9gT9I26KN4Yb;C;CMYnC5h3aA=*`0ZRg1Td*;D7R43cdc4mib[YhZZD4ENFnlhHd3`5CBWHh41;AUD[_Tach5?*cD9:hJXeQViXn|Lb8SYSA8cP[LGC(9A6f6ohDAQ=OM:dPg7GXV5U4]h3Q[:**KI(c[Y)B`BCFB|T|R]Y`X^*^?0=(9gG966Nj11DTdMR7N(6IEfDU5n6U3M2b^:W53mLQUBkbZH16Kj5b3LaDmJ::LGG*GIm65:f55h5GiJ7]kh?6jBhRCNRmEg*X:BSIRV1ZgHNF6K9^]*b`FAFoTbbR9WZ:Y]Ye]jIH*NC9Ga;bSXV|aaTk8J14;gI8Z0?IFm`:CIiQ)K0M0L4XSNDA=Y3UYL;16]40=6cmDHS^(7DVY*[KF_dek:5QVm()4QSg*4ZbUG[|ULE=b3Kd`Lg8VD390O^ISB0UlC=B=TROSKPaZA]4F|=T)abP):ODfi(]P(65;|OP8=BM0]MOcHIQTUYfZFmdg73|RfTViHMJT]b(k_3Sd`A^kASQNlNnIQT1HOjEW`5Zn|RInO_4:`:MmVP]n6oMI)?[1XmZV1a;1eF`FZLiXMG|2H^Rk6|d]JJ)V_J|mZcNk?ceOROHP4MbF3FVoFjR(*Dki)H9_P7962CXLYm;ScoLO;e`n]P*2MoO9Sd1SF`N)39da_XZG=FehN`SQhf[gOk|_kVLHYhECfFalYSRgQC?KT_HejCXNJn[7OUKdnE3=TBQOch:B1:?_mj[(^09M_a?^SDP4h?j(b9[Wa21_*HPCOJ^UolI0h0IN5TQaBeE5WgUV]B^k(QQ*h[=CW1aO?K3Ak6jU0ohgOBX_Yj3?gYGc0E[|?Wjm_ejCXlCOLc8)0fg7CmRg))d_K3(Z:b;EI5A)jf?jloG|nf)AWOb?^Zb5L5OEnmOWdXX^CbUHAiY2kO_21A^(MW^L^g=mc`7k86FS`.mmf

    Ici, ⨁ = ( x - 1 )( 2x + 4 ). On résout ( x - 1 )( 2x + 4 ) = 0 ⇔ x - 1 = 0  ou  2x + 4 = 0 ⇔ x = 1  ou  x = -2. Les racines du dénominateur sont donc 1 et -2. Ainsi Df = MMF.7h]V3`00QEM]Lm|f3?h5oPonZ=`Y?X8_4]E_SZMV_|EbcUKKgLgkX6EZjY]ONXZj]N_U_hlP:*Ub9Bm)HS`02N01*ESN;K)gjleZWRoGfNCkI;OHY?=l_*UFAOeYECc_WjJ?IOEb?QF7jHOmJOZgWW5n(mWUbo`Q3CiFaE)m?imVWn[S`FSOYi^]lA)XL1Z5DfHd?lgc=008YcZLLPI6bn4=Smi`=:Jo?Sk(UeU`(gVMk;IYWRncNlaQ^lgVZcAhme9FdfeIeo_C|eWmDPL|G:dFiJWnDWg;bWmL1:)6HCFoD7)W5YejOOSc_R[;_eZK7;9iMn[27CQe=1`l3_?m|GbI6]edLchFYmJR`lGiBkDgg)SjI7*mS;4NX*dS_)4JLKS674JX``Qg62L?`naQW3joY)n3lk5C7j7?[m7WenSc4OYlQ3hOYln7jO=anV;Tm(D8OG59gn[o=EN7Ql2M3264b^^==QC:bL;883f*1|AnTD83mhH83Ej)RBN=Rb8?4P)dUdd3*nQfO`i*ITk4=(3;W2c1==A()h1YP3NX=_9WVdFSS`dg=Q(NJH^hgin*83HAe*0PVG2|SYLa_1*Nf2[(_6O011XiXXja3R0JQ9F86Y3dT^)(TRHYL:a0dP11f75J0Zk85YX2Sk_L^)k7Y3D*=041Y232WT43A7^01TQj)Z[WG4AMG14ChT9Cg`T1TZHP(*G]7DQ)Z4Y1UdT:G0ZbFHPYg;I6g`e=ofQ2A2J4R6:d]FPJ2]?`naDm2RFaCiYfD?IJ=:aDA7]0HAKLbi[8BMMY4B(bJHF8MbF=J14R6kh1Z_(JAL*C7X9XlXRdIMbPY8|Bdl|*ddJ8BO`Hho_;44]KfMPSAKLPnBIVC5Xaa_SBbkH?OLXJ``__Bm?`f_EQP`*edDKD[P|J57GD=2I`flh3CBa9Ue[2R4c:Wg0B(A5MIA=9fS]Ai62BR6j9BLLTVX:4g31P[3MK6?*Qk`d^*BH?TaBXkX20mHHBRg]8dg818hd8`7ZfgVP4)iQJTk2UKHg^F[I*dHdA1G4X)h15^FeMmZYR1fAknV1796l0Yl3NS0K*T]PIbE]4c`K|V=*]8Zd1W5`)4?AcbXk9M|208?L3c:1TgD;KWdf6OU:ZMVW_M)b`K0]YYfF7fY;Lcao=AbH;KMZQ()l)^IQX1H_jE_?bE]]5eTkO`E^5fJFmG__ofThn]4[SDGR;IFVal5IU=Cnl_3FbFHaU5KOFf5[SWUEOgI]L[lKo50_`B0JcgZcGNL1ViSjaFFCn00GCI4IU?aN)7bnnOSPM3)ShS`nCcR065PllNCX3?WG)Zn[|en73i]gnE5CO78h=c|[WXRhMePI_bT)1glNL9S6JmdFe;ohhU=aWRaCBn|TSC3kmFUN5aic|N)]eHT0W1gCZ*ULL30=lS30gF]]OllW|PI6IUBdBf595eE|^DFg?1QGB[iCXa2aN?6c(HFCWjVRnU^KUem[gYg_1S=T)Gj`OeYO[c6WJW`71K3)KkWjacXfdOKL:|6c;;0o*gOKWmHNknCI5hb]jco8dbo7kj]gggN:g((B(kLo_`NKVeJci3fXO=AD.mmf \ { -2; 1 }.

     

    Autres Fonctions f(x) = ⊚

     

    Qu’est-ce donc que cette forme géométrique ?

    Le ⊚ au numérateur représente un terme plus ou moins complexe qui dépend bien évidemment de x.

    Pour f(x) = ( x + 4 )( x² - 2 ), nous avons tout simplement ⊚ = ( x + 4 )( x² - 2 )

    Quelle contrainte impose la fonction ?

    Cette fonction représente en fait toutes les fonctions ne correspondant pas aux 3 cas précédents. Cette fonction n'est pas identifiable à une fonction inverse, racine carrée ou logarithmique. Dans ce cas, aucune contrainte n'est imposée à x. Ainsi son domaine de définition sera l'ensemble des réels, Df = MMF.7h]V3`00QEM]Lm|f3?h5oPonZ=`Y?X8_4]E_SZMV_|EbcUKKgLgkX6EZjY]ONXZj]N_U_hlP:*Ub9Bm)HS`02N01*ESN;K)gjleZWRoGfNCkI;OHY?=l_*UFAOeYECc_WjJ?IOEb?QF7jHOmJOZgWW5n(mWUbo`Q3CiFaE)m?imVWn[S`FSOYi^]lA)XL1Z5DfHd?lgc=008YcZLLPI6bn4=Smi`=:Jo?Sk(UeU`(gVMk;IYWRncNlaQ^lgVZcAhme9FdfeIeo_C|eWmDPL|G:dFiJWnDWg;bWmL1:)6HCFoD7)W5YejOOSc_R[;_eZK7;9iMn[27CQe=1`l3_?m|GbI6]edLchFYmJR`lGiBkDgg)SjI7*mS;4NX*dS_)4JLKS674JX``Qg62L?`naQW3joY)n3lk5C7j7?[m7WenSc4OYlQ3hOYln7jO=anV;Tm(D8OG59gn[o=EN7Ql2M3264b^^==QC:bL;883f*1|AnTD83mhH83Ej)RBN=Rb8?4P)dUdd3*nQfO`i*ITk4=(3;W2c1==A()h1YP3NX=_9WVdFSS`dg=Q(NJH^hgin*83HAe*0PVG2|SYLa_1*Nf2[(_6O011XiXXja3R0JQ9F86Y3dT^)(TRHYL:a0dP11f75J0Zk85YX2Sk_L^)k7Y3D*=041Y232WT43A7^01TQj)Z[WG4AMG14ChT9Cg`T1TZHP(*G]7DQ)Z4Y1UdT:G0ZbFHPYg;I6g`e=ofQ2A2J4R6:d]FPJ2]?`naDm2RFaCiYfD?IJ=:aDA7]0HAKLbi[8BMMY4B(bJHF8MbF=J14R6kh1Z_(JAL*C7X9XlXRdIMbPY8|Bdl|*ddJ8BO`Hho_;44]KfMPSAKLPnBIVC5Xaa_SBbkH?OLXJ``__Bm?`f_EQP`*edDKD[P|J57GD=2I`flh3CBa9Ue[2R4c:Wg0B(A5MIA=9fS]Ai62BR6j9BLLTVX:4g31P[3MK6?*Qk`d^*BH?TaBXkX20mHHBRg]8dg818hd8`7ZfgVP4)iQJTk2UKHg^F[I*dHdA1G4X)h15^FeMmZYR1fAknV1796l0Yl3NS0K*T]PIbE]4c`K|V=*]8Zd1W5`)4?AcbXk9M|208?L3c:1TgD;KWdf6OU:ZMVW_M)b`K0]YYfF7fY;Lcao=AbH;KMZQ()l)^IQX1H_jE_?bE]]5eTkO`E^5fJFmG__ofThn]4[SDGR;IFVal5IU=Cnl_3FbFHaU5KOFf5[SWUEOgI]L[lKo50_`B0JcgZcGNL1ViSjaFFCn00GCI4IU?aN)7bnnOSPM3)ShS`nCcR065PllNCX3?WG)Zn[|en73i]gnE5CO78h=c|[WXRhMePI_bT)1glNL9S6JmdFe;ohhU=aWRaCBn|TSC3kmFUN5aic|N)]eHT0W1gCZ*ULL30=lS30gF]]OllW|PI6IUBdBf595eE|^DFg?1QGB[iCXa2aN?6c(HFCWjVRnU^KUem[gYg_1S=T)Gj`OeYO[c6WJW`71K3)KkWjacXfdOKL:|6c;;0o*gOKWmHNknCI5hb]jco8dbo7kj]gggN:g((B(kLo_`NKVeJci3fXO=AD.mmf .

    Exemple : f(x) = (x + 1)² + 4x + 5

    Ici, ⊚ = (x + 1)² + 4x + 5, nous identifions aucun des cas précédents. C'est pourquoi Df = MMF.7h]V3`00QEM]Lm|f3?h5oPonZ=`Y?X8_4]E_SZMV_|EbcUKKgLgkX6EZjY]ONXZj]N_U_hlP:*Ub9Bm)HS`02N01*ESN;K)gjleZWRoGfNCkI;OHY?=l_*UFAOeYECc_WjJ?IOEb?QF7jHOmJOZgWW5n(mWUbo`Q3CiFaE)m?imVWn[S`FSOYi^]lA)XL1Z5DfHd?lgc=008YcZLLPI6bn4=Smi`=:Jo?Sk(UeU`(gVMk;IYWRncNlaQ^lgVZcAhme9FdfeIeo_C|eWmDPL|G:dFiJWnDWg;bWmL1:)6HCFoD7)W5YejOOSc_R[;_eZK7;9iMn[27CQe=1`l3_?m|GbI6]edLchFYmJR`lGiBkDgg)SjI7*mS;4NX*dS_)4JLKS674JX``Qg62L?`naQW3joY)n3lk5C7j7?[m7WenSc4OYlQ3hOYln7jO=anV;Tm(D8OG59gn[o=EN7Ql2M3264b^^==QC:bL;883f*1|AnTD83mhH83Ej)RBN=Rb8?4P)dUdd3*nQfO`i*ITk4=(3;W2c1==A()h1YP3NX=_9WVdFSS`dg=Q(NJH^hgin*83HAe*0PVG2|SYLa_1*Nf2[(_6O011XiXXja3R0JQ9F86Y3dT^)(TRHYL:a0dP11f75J0Zk85YX2Sk_L^)k7Y3D*=041Y232WT43A7^01TQj)Z[WG4AMG14ChT9Cg`T1TZHP(*G]7DQ)Z4Y1UdT:G0ZbFHPYg;I6g`e=ofQ2A2J4R6:d]FPJ2]?`naDm2RFaCiYfD?IJ=:aDA7]0HAKLbi[8BMMY4B(bJHF8MbF=J14R6kh1Z_(JAL*C7X9XlXRdIMbPY8|Bdl|*ddJ8BO`Hho_;44]KfMPSAKLPnBIVC5Xaa_SBbkH?OLXJ``__Bm?`f_EQP`*edDKD[P|J57GD=2I`flh3CBa9Ue[2R4c:Wg0B(A5MIA=9fS]Ai62BR6j9BLLTVX:4g31P[3MK6?*Qk`d^*BH?TaBXkX20mHHBRg]8dg818hd8`7ZfgVP4)iQJTk2UKHg^F[I*dHdA1G4X)h15^FeMmZYR1fAknV1796l0Yl3NS0K*T]PIbE]4c`K|V=*]8Zd1W5`)4?AcbXk9M|208?L3c:1TgD;KWdf6OU:ZMVW_M)b`K0]YYfF7fY;Lcao=AbH;KMZQ()l)^IQX1H_jE_?bE]]5eTkO`E^5fJFmG__ofThn]4[SDGR;IFVal5IU=Cnl_3FbFHaU5KOFf5[SWUEOgI]L[lKo50_`B0JcgZcGNL1ViSjaFFCn00GCI4IU?aN)7bnnOSPM3)ShS`nCcR065PllNCX3?WG)Zn[|en73i]gnE5CO78h=c|[WXRhMePI_bT)1glNL9S6JmdFe;ohhU=aWRaCBn|TSC3kmFUN5aic|N)]eHT0W1gCZ*ULL30=lS30gF]]OllW|PI6IUBdBf595eE|^DFg?1QGB[iCXa2aN?6c(HFCWjVRnU^KUem[gYg_1S=T)Gj`OeYO[c6WJW`71K3)KkWjacXfdOKL:|6c;;0o*gOKWmHNknCI5hb]jco8dbo7kj]gggN:g((B(kLo_`NKVeJci3fXO=AD.mmf .

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    ↬ Certaines fonctions correspondent à un mixte de cas, il faudra alors prendre en compte les contraintes de chacun des cas. Par exemple, pour f(x) = 1 x-1 MMF.7h]`3`00QEO=L]]637h2_h))m0b]FN`?^La=EQUGDd_bB8cCPbm|b[ZJfU9::fdBSmnm`)jB11EB]F`;7k0;h(=R8NYQ|GZogRaWaF:m^WRmN9Q_lUVagTC;l_SW|WcLOI[LEOG;HElnCCk^mY=ok5C:bh^7HU7LiU7nmiOb^3_|[`1EmoUVRdhR4dnBN29*lm)|b2)0N6;SRAB0FPW_Y7ZWbISoNWLkFjbRbh^gRhM]GQB;e*dU|=f^I||ln_1BeI=]MCc^mXnhn^DHRGRiW5OkhiOjfj[jedM0=*b[iHUJN[GZe)^WgfoZZ_Z[]NTQFg1WC]b1EbO3`M)hf3eG;a?DCCJ7ig;OFV`l?gbYMlR=[lm6el(Hja7J((8KcQ67LlaQQ3Z(L8MalS3(7|KYbe?j8KPL)oDAn_8LOGV)_QbQ;dOXbg7jLYRn7:N_ATiOSM1GYoBMoS]N7AV3m3;449^PAff|S9LEbZ03d0SB|(R***I3*XHPYlbCYDE901T26fA|H8Smk|lAbL:;U0H4FK8UU8JIFPlX3*P6ddKnk;9Xm2Ub4e(ET7E8Q_dI2n8B(*d0UXVTjPBI`V|EP:_2=7P6BZ2A4njHjP2Z*EB9Y05I;cTY)6VFPZ*:I0e*S9gT9I26KN4Yb;C;CMYnC5h3aA=*`0ZRg1Td*;D7R43cdc4mib[YhZZD4ENFnlhHd3`5CBWHh41;AUD[_Tach5?*cD9:hJXeQViXn|Lb8SYSA8cP[LGC(9A6f6ohDAQ=OM:dPg7GXV5U4]h3Q[:**KI(c[Y)B`BCFB|T|R]Y`X^*^?0=(9gG966Nj11DTdMR7N(6IEfDU5n6U3M2b^:W53mLQUBkbZH16Kj5b3LaDmJ::LGG*GIm65:f55h5GiJ7]kh?6jBhRCNRmEg*X:BSIRV1ZgHNF6K9^]*b`FAFoTbbR9WZ:Y]Ye]jIH*NC9Ga;bSXV|aaTk8J14;gI8Z0?IFm`:CIiQ)K0M0L4XSNDA=Y3UYL;16]40=6cmDHS^(7DVY*[KF_dek:5QVm()4QSg*4ZbUG[|ULE=b3Kd`Lg8VD390O^ISB0UlC=B=TROSKPaZA]4F|=T)abP):ODfi(]P(65;|OP8=BM0]MOcHIQTUYfZFmdg73|RfTViHMJT]b(k_3Sd`A^kASQNlNnIQT1HOjEW`5Zn|RInO_4:`:MmVP]n6oMI)?[1XmZV1a;1eF`FZLiXMG|2H^Rk6|d]JJ)V_J|mZcNk?ceOROHP4MbF3FVoFjR(*Dki)H9_P7962CXLYm;ScoLO;e`n]P*2MoO9Sd1SF`N)39da_XZG=FehN`SQhf[gOk|_kVLHYhECfFalYSRgQC?KT_HejCXNJn[7OUKdnE3=TBQOch:B1:?_mj[(^09M_a?^SDP4h?j(b9[Wa21_*HPCOJ^UolI0h0IN5TQaBeE5WgUV]B^k(QQ*h[=CW1aO?K3Ak6jU0ohgOBX_Yj3?gYGc0E[|?Wjm_ejCXlCOLc8)0fg7CmRg))d_K3(Z:b;EI5A)jf?jloG|nf)AWOb?^Zb5L5OEnmOWdXX^CbUHAiY2kO_21A^(MW^L^g=mc`7k86FS`.mmf , nous devons avoir x - 1 ≥ 0 (contrainte de la racine) et x - 1 ≠ 0 (contrainte de l'inverse). Ainsi en regroupant ces 2 contraintes, nous obtenons x - 1 > 0 , d'où Df = 1 ; + MMF.7h_N3`00QEMOLn963?l4n*hlVQV7FNdONgem8]BG(PdV0kiL7gQa[fk:=86[`kEgcNBkEeZ_KIVcJDR2OY9FdTn[GLa^VKeOKeKcO;W)[Uj_MX]=)|oGVf1EW?iH5HokCi?k|WXi7XZWbLOmHO:gWDTi_M[Ubo`^3M:o_QBWoO5`3JQjB3MK31:HL1:54h6J7nMi6P244jW`C`2Z8GjWTWMBXcGmiOi^_|b2jMGKeFjKi_Tb^jD:]]]|_TZ33bmU=MVFYm?nl8SN;jM0Q:_EXSbL_UCO|_:O)PFZHEP]cmBbEZ])_GkjkKHZbcmKVajbnG3V;1cDjVPhNAcVnnObIH:jbNKhG1aJR`dGaboE7[UaofCD7lIHSm264Mi`RCQLHPhSe664)hbCQf7f(4iOW]?gbNGH[Xo*UiOXbd_di*Qm)D9OS])G`oCU)7de|_]ZQ;hjYnodon;ATB78FXH**^?eZ0fEZFF5(VP?=8;H)aTbB6n8b)3UV4Fbi1AiT22`G|H1Q[1NoCTPFM*RU*5NU|b5bS0cF`(Z0kc1]9To^bXJOHcLa4aiI1fBOWg2T[Q2C0)0EB:Y)ejVm5Yih;X`li612VSTR0NV?X1Z47DRJT3B:dh:CYZE8:T3B*(DHbMi2jAQBgP9(^iZTkJOToM0l*8D|8HX]`L=D)d68]1lMd`_^8Zj_2YVa9GU|A(6=2m1D`WF1m2BDMF:^fT)jQ9dhdPUG;M6?`g=o5Q6A2N(R15l]7PIQ|[`j`gO2Z=YCYYa()iH=:a(a6O0D1GBbiK9BCMYTF0b6hE8MRf=N1(RUkh1YX|JAB`BKH9ZjXR|HmbPY(|Bll(*ld68FOjHl__346_GfMPS`iL*nBIWc4HaY_cJbfh)OLVFdR|Obo;d]Yk31RU^hX=XjbUXD=AA|eC0MG|OF6I9^]8B`FCFoTBbS8WZ)Y]X=]j9HA^CA7a9c2HV|A`Tk8B14;fkAD0Ob]k5YMS=8c*7Y]|P4;e;BL*mI7Vk*;11110mFnmZ17La]BKUF]|Jjf?I*|(GAQc4XNh0=NFj3MW[R[|Pfmd7MdG:1TP)g(UX06n9^b=URoSNP;|VKH_HJ81TQ`(DoiabefAk`H1Ri`?`XQBMXi_?YT9oDi[F]KLkk[9|6nU^b`je;KVMgn=7YPQMfJ72ma[E)LT:3_F]n?9F=dG)c]o1FaF^|Ui_oGo[KSjbJXbX_(FaM5QiZg6JkekN6[TZaZZ:Ff_|[77?JRn^CBighgnJ1K*UPeE_e^|l43(lCf8FhAn*P4)6:_Nil?ckfMN?FPL3)_Wm`fA]D0?)0dnN]H6N)^MEMOAnm;1i|clDeKLJahRcl[4hUCFfR3OUTo|fEV|Be3`DeKkhmJVD_UZRT9hnNDC5Yem?EN6aI2_NNidJd)T1WCWC5Do8P1hSl4AKmh^Oc1jP;9c|T::A:ZZN^bJefa]BJ)nY:*Pj;nhf^1WI|G[6;jEinOGTik=n`Dbh2En|kmKWO[RKkVM0`6Fhj)IW5abUkHME*6eKIWU0hKHo[CoNc;LY6MlXNYJWFDkOEfmNMgU07lJ_:;k]7X9Xn[KKhW(GC)U=a]?M8_QQbY`Jj`8cM0|0bJ4C=4iTgFgaZ3TOn^o2K?51bkJA)go_m8KEo*LMF:Dk.mmf

    ↬ L'énoncé d'un exercice peut vous imposer des contraintes sur x. C'est le cas avec les exercices types géométrique et économique du chapitre polynôme du second degré.

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    Un peu de Théorie

    Fonction Racine f(x) = MMF.7h]Z3`00QEO=L]]637h2_h))m0b]FN`?^La=EQUGDh_bB8cCPbi(b[ZJfU9:bfdBSmnm`799PPZYF9J=3l1RlF6a4;EMI)mGjnD|GjbbRmN;kGbMc_;E)UPFaknFaL?^lnB^[9h?nn9alW6gWoa[Ye9NGVccAGjK1^To;lEaMmQO0J[^doD6P`*VW4CQA:3VUeVN1R32RMCh5X1Z|)o0_=(J[NW_MkNcAAILG[aMK3MYWRnb6lYP|lUVbcChl5aFTdei?)kf3nSmO0a4^5c)bogaYOZFUOoEFj0JQ]GbA2e[]N[DZlLoKZZbo;^ejB6K3fM)`T6]SXHgSl=lme*nCe0gFAnNRWe[|N7ll5;]T1_gCdKmHHce26dHh*gWR((iiS127DJh`cQi66H?hoCU:Gfo^A`kmA7jlQamNHjn7:4_AnS;LOYbV;hLYjm6CUn=d5NWm9gn)ehM6H:|I*PQ=5j?fU2IFUHXPoI08hRmTb63m8J835j)FBA;CY472*;[IFaP2)_EG`:BABeB6^1UbE`X3C)e=J0d`1](^o(GUdFSSi6KV2Z?[4?B[doH9RhAd`1PVDRZSYMYNjdlL5FHn|Q02CAba0=C7D0eR2XA=B3Y9BL59leBT5B1Y06:|I)l1=:`9C`56GNiBM_OTmM0l**D|88XM`H=D)d18]3lM4`_^8ZjOEG(R2_;HbL(J9j2YQB|3j0UXjXEMm(Le2WXaY5B^6Z=_Q^Jo[6(R4hH4B=hJo4d3:GQea]n54ICWcC]H=beJ5RIR?N0XBbTUbfCTjkC8|5TePZAk4XJlB94K_|6V2iZ5;58M0RZbB)bSW63TVjGV5n6V3M2c?J?JGmo6F;]:Q]kI?PB8]o|6K=FS6UokFGGQciUBm|[7l_bkFgMQ`eBg(*KdMIMd:2XXfHYPJ]f7UQVBK[D4|5TE_i4|QdCeEDfdJbm4l()9XWhTYQeC68iB=P=0b5j|dE07l[Nh59|lPS=PNT)24A_:8VhQb`_5`SFR02RIn^=AW23ZCDYEm[FF5o;5QZn()8P3WD7Z2QGKLQNEMb0K4lOg8RD3I0L^9_A05hB=b=URoSIP1^C]TF|=D2bb`6:Odji(MT)653|OP0)B]4i^_i|(_BCd[B^_M=a`k8]Y9^F7FY;LS)k`hm(4KZd*hGoJeC_BEI`Z6o5UkNj;W9foQnlEN4ZjoGFokE^lY5EHdCU;HjU`lYKSM?ll?;Fb6DaUUGLFV=WSG]FNgI]L[hJ?bTFd94(I[eN[O90C?4nRFV4Kb01V`aEkW?QjLnC[ane3PIdl|N7bMZP1Y`7WSa[0ceecZ[Zh?gXHO=j]bnZKcF)4FOU*g4|Jf`A[l]7mff|eRBX^BnZGO7Y|I*nFj:*7SmkA(VWGhmEhK5T:mikWA[*j*6M)M4ESlR07R?`AU_gRio(7Z0|W)b*XYHZZYjk9[Dk6e9XkjTY23[?KmMh6=VQN|8_YGWimNSk|gk1E;P)Wjm^EjMnN9[^Id30IKSXnSLG7:G=QfE0IE]TND3Q=[n^?Uk?=RTIgbQjUZMIC]mG[eng)AECG;jB?0odiM_f7_gNg]3cOeEd0IX.mmf

    Qu’est-ce donc que cette forme géométrique ?

    Le ∎ sous la racine représente un terme plus ou moins complexe qui dépend bien évidemment de x.

    Pour f(x) = (x+4)(x²-2) MMF.7h]Z3`00QEO=L]]637h2_h))m0b]FN`?^La=EQUGDh_bB8cCPbi(b[ZJfU9:bfdBSmnm`799PPZYF9J=3l1RlF6a4;EMI)mGjnD|GjbbRmN;kGbMc_;E)UPFaknFaL?^lnB^[9h?nn9alW6gWoa[Ye9NGVccAGjK1^To;lEaMmQO0J[^doD6P`*VW4CQA:3VUeVN1R32RMCh5X1Z|)o0_=(J[NW_MkNcAAILG[aMK3MYWRnb6lYP|lUVbcChl5aFTdei?)kf3nSmO0a4^5c)bogaYOZFUOoEFj0JQ]GbA2e[]N[DZlLoKZZbo;^ejB6K3fM)`T6]SXHgSl=lme*nCe0gFAnNRWe[|N7ll5;]T1_gCdKmHHce26dHh*gWR((iiS127DJh`cQi66H?hoCU:Gfo^A`kmA7jlQamNHjn7:4_AnS;LOYbV;hLYjm6CUn=d5NWm9gn)ehM6H:|I*PQ=5j?fU2IFUHXPoI08hRmTb63m8J835j)FBA;CY472*;[IFaP2)_EG`:BABeB6^1UbE`X3C)e=J0d`1](^o(GUdFSSi6KV2Z?[4?B[doH9RhAd`1PVDRZSYMYNjdlL5FHn|Q02CAba0=C7D0eR2XA=B3Y9BL59leBT5B1Y06:|I)l1=:`9C`56GNiBM_OTmM0l**D|88XM`H=D)d18]3lM4`_^8ZjOEG(R2_;HbL(J9j2YQB|3j0UXjXEMm(Le2WXaY5B^6Z=_Q^Jo[6(R4hH4B=hJo4d3:GQea]n54ICWcC]H=beJ5RIR?N0XBbTUbfCTjkC8|5TePZAk4XJlB94K_|6V2iZ5;58M0RZbB)bSW63TVjGV5n6V3M2c?J?JGmo6F;]:Q]kI?PB8]o|6K=FS6UokFGGQciUBm|[7l_bkFgMQ`eBg(*KdMIMd:2XXfHYPJ]f7UQVBK[D4|5TE_i4|QdCeEDfdJbm4l()9XWhTYQeC68iB=P=0b5j|dE07l[Nh59|lPS=PNT)24A_:8VhQb`_5`SFR02RIn^=AW23ZCDYEm[FF5o;5QZn()8P3WD7Z2QGKLQNEMb0K4lOg8RD3I0L^9_A05hB=b=URoSIP1^C]TF|=D2bb`6:Odji(MT)653|OP0)B]4i^_i|(_BCd[B^_M=a`k8]Y9^F7FY;LS)k`hm(4KZd*hGoJeC_BEI`Z6o5UkNj;W9foQnlEN4ZjoGFokE^lY5EHdCU;HjU`lYKSM?ll?;Fb6DaUUGLFV=WSG]FNgI]L[hJ?bTFd94(I[eN[O90C?4nRFV4Kb01V`aEkW?QjLnC[ane3PIdl|N7bMZP1Y`7WSa[0ceecZ[Zh?gXHO=j]bnZKcF)4FOU*g4|Jf`A[l]7mff|eRBX^BnZGO7Y|I*nFj:*7SmkA(VWGhmEhK5T:mikWA[*j*6M)M4ESlR07R?`AU_gRio(7Z0|W)b*XYHZZYjk9[Dk6e9XkjTY23[?KmMh6=VQN|8_YGWimNSk|gk1E;P)Wjm^EjMnN9[^Id30IKSXnSLG7:G=QfE0IE]TND3Q=[n^?Uk?=RTIgbQjUZMIC]mG[eng)AECG;jB?0odiM_f7_gNg]3cOeEd0IX.mmf , nous avons ∎ = ( x + 4 )( x² - 2 )

    Quelle contrainte impose la fonction ?

    Tout ce qui se trouve sous une racine carrée doit être positif ou nul, ainsi nous avons forcément ∎ ≥ 0. Nous obtenons alors le domaine de définition en résolvant cette inéquation grâce à un tableau de signes.

    Exemple : f(x) = x² - 4 MMF.7h]Z3`00QEO=L]]637h2_h))m0b]FN`?^La=EQUGDh_bB8cCPbi(b[ZJfU9:bfdBSmnm`799PPZYF9J=3l1RlF6a4;EMI)mGjnD|GjbbRmN;kGbMc_;E)UPFaknFaL?^lnB^[9h?nn9alW6gWoa[Ye9NGVccAGjK1^To;lEaMmQO0J[^doD6P`*VW4CQA:3VUeVN1R32RMCh5X1Z|)o0_=(J[NW_MkNcAAILG[aMK3MYWRnb6lYP|lUVbcChl5aFTdei?)kf3nSmO0a4^5c)bogaYOZFUOoEFj0JQ]GbA2e[]N[DZlLoKZZbo;^ejB6K3fM)`T6]SXHgSl=lme*nCe0gFAnNRWe[|N7ll5;]T1_gCdKmHHce26dHh*gWR((iiS127DJh`cQi66H?hoCU:Gfo^A`kmA7jlQamNHjn7:4_AnS;LOYbV;hLYjm6CUn=d5NWm9gn)ehM6H:|I*PQ=5j?fU2IFUHXPoI08hRmTb63m8J835j)FBA;CY472*;[IFaP2)_EG`:BABeB6^1UbE`X3C)e=J0d`1](^o(GUdFSSi6KV2Z?[4?B[doH9RhAd`1PVDRZSYMYNjdlL5FHn|Q02CAba0=C7D0eR2XA=B3Y9BL59leBT5B1Y06:|I)l1=:`9C`56GNiBM_OTmM0l**D|88XM`H=D)d18]3lM4`_^8ZjOEG(R2_;HbL(J9j2YQB|3j0UXjXEMm(Le2WXaY5B^6Z=_Q^Jo[6(R4hH4B=hJo4d3:GQea]n54ICWcC]H=beJ5RIR?N0XBbTUbfCTjkC8|5TePZAk4XJlB94K_|6V2iZ5;58M0RZbB)bSW63TVjGV5n6V3M2c?J?JGmo6F;]:Q]kI?PB8]o|6K=FS6UokFGGQciUBm|[7l_bkFgMQ`eBg(*KdMIMd:2XXfHYPJ]f7UQVBK[D4|5TE_i4|QdCeEDfdJbm4l()9XWhTYQeC68iB=P=0b5j|dE07l[Nh59|lPS=PNT)24A_:8VhQb`_5`SFR02RIn^=AW23ZCDYEm[FF5o;5QZn()8P3WD7Z2QGKLQNEMb0K4lOg8RD3I0L^9_A05hB=b=URoSIP1^C]TF|=D2bb`6:Odji(MT)653|OP0)B]4i^_i|(_BCd[B^_M=a`k8]Y9^F7FY;LS)k`hm(4KZd*hGoJeC_BEI`Z6o5UkNj;W9foQnlEN4ZjoGFokE^lY5EHdCU;HjU`lYKSM?ll?;Fb6DaUUGLFV=WSG]FNgI]L[hJ?bTFd94(I[eN[O90C?4nRFV4Kb01V`aEkW?QjLnC[ane3PIdl|N7bMZP1Y`7WSa[0ceecZ[Zh?gXHO=j]bnZKcF)4FOU*g4|Jf`A[l]7mff|eRBX^BnZGO7Y|I*nFj:*7SmkA(VWGhmEhK5T:mikWA[*j*6M)M4ESlR07R?`AU_gRio(7Z0|W)b*XYHZZYjk9[Dk6e9XkjTY23[?KmMh6=VQN|8_YGWimNSk|gk1E;P)Wjm^EjMnN9[^Id30IKSXnSLG7:G=QfE0IE]TND3Q=[n^?Uk?=RTIgbQjUZMIC]mG[eng)AECG;jB?0odiM_f7_gNg]3cOeEd0IX.mmf

    Ici, ∎ = x² - 4 . Ainsi on résout x² - 4 ≥ 0. Ce polynôme du second degré est du signe de a = 1 positif, sauf entre ses racines -2 et 2. On obtient donc que x² - 4 ≥ 0 quand x ∈ ; 2 MMF.7h_N3`00QEMOLn963?l4n*hlVQV7FNdONgem8]BG(PdV0kiL7gQa[fk:=86[`kEgcNBkEeZ_KIVcJDR2OY9FdTn[GLa^VKeOKeKcO;W)[Uj_MX]=)|oGVf1EW?iH5HokCi?k|WXi7XZWbLOmHO:gWDTi_M[Ubo`^3M:o_QBWoO5`3JQjB3MK31:HL1:54h6J7nMi6P244jW`C`2Z8GjWTWMBXcGmiOi^_|b2jMGKeFjKi_Tb^jD:]]]|_TZ33bmU=MVFYm?nl8SN;jM0Q:_EXSbL_UCO|_:O)PFZHEP]cmBbEZ])_GkjkKHZbcmKVajbnG3V;1cDjVPhNAcVnnObIH:jbNKhG1aJR`dGaboE7[UaofCD7lIHSm264Mi`RCQLHPhSe664)hbCQf7f(4iOW]?gbNGH[Xo*UiOXbd_di*Qm)D9OS])G`oCU)7de|_]ZQ;hjYnodon;ATB78FXH**^?eZ0fEZFF5(VP?=8;H)aTbB6n8b)3UV4Fbi1AiT22`G|H1Q[1NoCTPFM*RU*5NU|b5bS0cF`(Z0kc1]9To^bXJOHcLa4aiI1fBOWg2T[Q2C0)0EB:Y)ejVm5Yih;X`li612VSTR0NV?X1Z47DRJT3B:dh:CYZE8:T3B*(DHbMi2jAQBgP9(^iZTkJOToM0l*8D|8HX]`L=D)d68]1lMd`_^8Zj_2YVa9GU|A(6=2m1D`WF1m2BDMF:^fT)jQ9dhdPUG;M6?`g=o5Q6A2N(R15l]7PIQ|[`j`gO2Z=YCYYa()iH=:a(a6O0D1GBbiK9BCMYTF0b6hE8MRf=N1(RUkh1YX|JAB`BKH9ZjXR|HmbPY(|Bll(*ld68FOjHl__346_GfMPS`iL*nBIWc4HaY_cJbfh)OLVFdR|Obo;d]Yk31RU^hX=XjbUXD=AA|eC0MG|OF6I9^]8B`FCFoTBbS8WZ)Y]X=]j9HA^CA7a9c2HV|A`Tk8B14;fkAD0Ob]k5YMS=8c*7Y]|P4;e;BL*mI7Vk*;11110mFnmZ17La]BKUF]|Jjf?I*|(GAQc4XNh0=NFj3MW[R[|Pfmd7MdG:1TP)g(UX06n9^b=URoSNP;|VKH_HJ81TQ`(DoiabefAk`H1Ri`?`XQBMXi_?YT9oDi[F]KLkk[9|6nU^b`je;KVMgn=7YPQMfJ72ma[E)LT:3_F]n?9F=dG)c]o1FaF^|Ui_oGo[KSjbJXbX_(FaM5QiZg6JkekN6[TZaZZ:Ff_|[77?JRn^CBighgnJ1K*UPeE_e^|l43(lCf8FhAn*P4)6:_Nil?ckfMN?FPL3)_Wm`fA]D0?)0dnN]H6N)^MEMOAnm;1i|clDeKLJahRcl[4hUCFfR3OUTo|fEV|Be3`DeKkhmJVD_UZRT9hnNDC5Yem?EN6aI2_NNidJd)T1WCWC5Do8P1hSl4AKmh^Oc1jP;9c|T::A:ZZN^bJefa]BJ)nY:*Pj;nhf^1WI|G[6;jEinOGTik=n`Dbh2En|kmKWO[RKkVM0`6Fhj)IW5abUkHME*6eKIWU0hKHo[CoNc;LY6MlXNYJWFDkOEfmNMgU07lJ_:;k]7X9Xn[KKhW(GC)U=a]?M8_QQbY`Jj`8cM0|0bJ4C=4iTgFgaZ3TOn^o2K?51bkJA)go_m8KEo*LMF:Dk.mmf 2 ; + MMF.7h_N3`00QEMOLn963?l4n*hlVQV7FNdONgem8]BG(PdV0kiL7gQa[fk:=86[`kEgcNBkEeZ_KIVcJDR2OY9FdTn[GLa^VKeOKeKcO;W)[Uj_MX]=)|oGVf1EW?iH5HokCi?k|WXi7XZWbLOmHO:gWDTi_M[Ubo`^3M:o_QBWoO5`3JQjB3MK31:HL1:54h6J7nMi6P244jW`C`2Z8GjWTWMBXcGmiOi^_|b2jMGKeFjKi_Tb^jD:]]]|_TZ33bmU=MVFYm?nl8SN;jM0Q:_EXSbL_UCO|_:O)PFZHEP]cmBbEZ])_GkjkKHZbcmKVajbnG3V;1cDjVPhNAcVnnObIH:jbNKhG1aJR`dGaboE7[UaofCD7lIHSm264Mi`RCQLHPhSe664)hbCQf7f(4iOW]?gbNGH[Xo*UiOXbd_di*Qm)D9OS])G`oCU)7de|_]ZQ;hjYnodon;ATB78FXH**^?eZ0fEZFF5(VP?=8;H)aTbB6n8b)3UV4Fbi1AiT22`G|H1Q[1NoCTPFM*RU*5NU|b5bS0cF`(Z0kc1]9To^bXJOHcLa4aiI1fBOWg2T[Q2C0)0EB:Y)ejVm5Yih;X`li612VSTR0NV?X1Z47DRJT3B:dh:CYZE8:T3B*(DHbMi2jAQBgP9(^iZTkJOToM0l*8D|8HX]`L=D)d68]1lMd`_^8Zj_2YVa9GU|A(6=2m1D`WF1m2BDMF:^fT)jQ9dhdPUG;M6?`g=o5Q6A2N(R15l]7PIQ|[`j`gO2Z=YCYYa()iH=:a(a6O0D1GBbiK9BCMYTF0b6hE8MRf=N1(RUkh1YX|JAB`BKH9ZjXR|HmbPY(|Bll(*ld68FOjHl__346_GfMPS`iL*nBIWc4HaY_cJbfh)OLVFdR|Obo;d]Yk31RU^hX=XjbUXD=AA|eC0MG|OF6I9^]8B`FCFoTBbS8WZ)Y]X=]j9HA^CA7a9c2HV|A`Tk8B14;fkAD0Ob]k5YMS=8c*7Y]|P4;e;BL*mI7Vk*;11110mFnmZ17La]BKUF]|Jjf?I*|(GAQc4XNh0=NFj3MW[R[|Pfmd7MdG:1TP)g(UX06n9^b=URoSNP;|VKH_HJ81TQ`(DoiabefAk`H1Ri`?`XQBMXi_?YT9oDi[F]KLkk[9|6nU^b`je;KVMgn=7YPQMfJ72ma[E)LT:3_F]n?9F=dG)c]o1FaF^|Ui_oGo[KSjbJXbX_(FaM5QiZg6JkekN6[TZaZZ:Ff_|[77?JRn^CBighgnJ1K*UPeE_e^|l43(lCf8FhAn*P4)6:_Nil?ckfMN?FPL3)_Wm`fA]D0?)0dnN]H6N)^MEMOAnm;1i|clDeKLJahRcl[4hUCFfR3OUTo|fEV|Be3`DeKkhmJVD_UZRT9hnNDC5Yem?EN6aI2_NNidJd)T1WCWC5Do8P1hSl4AKmh^Oc1jP;9c|T::A:ZZN^bJefa]BJ)nY:*Pj;nhf^1WI|G[6;jEinOGTik=n`Dbh2En|kmKWO[RKkVM0`6Fhj)IW5abUkHME*6eKIWU0hKHo[CoNc;LY6MlXNYJWFDkOEfmNMgU07lJ_:;k]7X9Xn[KKhW(GC)U=a]?M8_QQbY`Jj`8cM0|0bJ4C=4iTgFgaZ3TOn^o2K?51bkJA)go_m8KEo*LMF:Dk.mmf . Ainsi Df = ; 2 MMF.7h_N3`00QEMOLn963?l4n*hlVQV7FNdONgem8]BG(PdV0kiL7gQa[fk:=86[`kEgcNBkEeZ_KIVcJDR2OY9FdTn[GLa^VKeOKeKcO;W)[Uj_MX]=)|oGVf1EW?iH5HokCi?k|WXi7XZWbLOmHO:gWDTi_M[Ubo`^3M:o_QBWoO5`3JQjB3MK31:HL1:54h6J7nMi6P244jW`C`2Z8GjWTWMBXcGmiOi^_|b2jMGKeFjKi_Tb^jD:]]]|_TZ33bmU=MVFYm?nl8SN;jM0Q:_EXSbL_UCO|_:O)PFZHEP]cmBbEZ])_GkjkKHZbcmKVajbnG3V;1cDjVPhNAcVnnObIH:jbNKhG1aJR`dGaboE7[UaofCD7lIHSm264Mi`RCQLHPhSe664)hbCQf7f(4iOW]?gbNGH[Xo*UiOXbd_di*Qm)D9OS])G`oCU)7de|_]ZQ;hjYnodon;ATB78FXH**^?eZ0fEZFF5(VP?=8;H)aTbB6n8b)3UV4Fbi1AiT22`G|H1Q[1NoCTPFM*RU*5NU|b5bS0cF`(Z0kc1]9To^bXJOHcLa4aiI1fBOWg2T[Q2C0)0EB:Y)ejVm5Yih;X`li612VSTR0NV?X1Z47DRJT3B:dh:CYZE8:T3B*(DHbMi2jAQBgP9(^iZTkJOToM0l*8D|8HX]`L=D)d68]1lMd`_^8Zj_2YVa9GU|A(6=2m1D`WF1m2BDMF:^fT)jQ9dhdPUG;M6?`g=o5Q6A2N(R15l]7PIQ|[`j`gO2Z=YCYYa()iH=:a(a6O0D1GBbiK9BCMYTF0b6hE8MRf=N1(RUkh1YX|JAB`BKH9ZjXR|HmbPY(|Bll(*ld68FOjHl__346_GfMPS`iL*nBIWc4HaY_cJbfh)OLVFdR|Obo;d]Yk31RU^hX=XjbUXD=AA|eC0MG|OF6I9^]8B`FCFoTBbS8WZ)Y]X=]j9HA^CA7a9c2HV|A`Tk8B14;fkAD0Ob]k5YMS=8c*7Y]|P4;e;BL*mI7Vk*;11110mFnmZ17La]BKUF]|Jjf?I*|(GAQc4XNh0=NFj3MW[R[|Pfmd7MdG:1TP)g(UX06n9^b=URoSNP;|VKH_HJ81TQ`(DoiabefAk`H1Ri`?`XQBMXi_?YT9oDi[F]KLkk[9|6nU^b`je;KVMgn=7YPQMfJ72ma[E)LT:3_F]n?9F=dG)c]o1FaF^|Ui_oGo[KSjbJXbX_(FaM5QiZg6JkekN6[TZaZZ:Ff_|[77?JRn^CBighgnJ1K*UPeE_e^|l43(lCf8FhAn*P4)6:_Nil?ckfMN?FPL3)_Wm`fA]D0?)0dnN]H6N)^MEMOAnm;1i|clDeKLJahRcl[4hUCFfR3OUTo|fEV|Be3`DeKkhmJVD_UZRT9hnNDC5Yem?EN6aI2_NNidJd)T1WCWC5Do8P1hSl4AKmh^Oc1jP;9c|T::A:ZZN^bJefa]BJ)nY:*Pj;nhf^1WI|G[6;jEinOGTik=n`Dbh2En|kmKWO[RKkVM0`6Fhj)IW5abUkHME*6eKIWU0hKHo[CoNc;LY6MlXNYJWFDkOEfmNMgU07lJ_:;k]7X9Xn[KKhW(GC)U=a]?M8_QQbY`Jj`8cM0|0bJ4C=4iTgFgaZ3TOn^o2K?51bkJA)go_m8KEo*LMF:Dk.mmf 2 ; + MMF.7h_N3`00QEMOLn963?l4n*hlVQV7FNdONgem8]BG(PdV0kiL7gQa[fk:=86[`kEgcNBkEeZ_KIVcJDR2OY9FdTn[GLa^VKeOKeKcO;W)[Uj_MX]=)|oGVf1EW?iH5HokCi?k|WXi7XZWbLOmHO:gWDTi_M[Ubo`^3M:o_QBWoO5`3JQjB3MK31:HL1:54h6J7nMi6P244jW`C`2Z8GjWTWMBXcGmiOi^_|b2jMGKeFjKi_Tb^jD:]]]|_TZ33bmU=MVFYm?nl8SN;jM0Q:_EXSbL_UCO|_:O)PFZHEP]cmBbEZ])_GkjkKHZbcmKVajbnG3V;1cDjVPhNAcVnnObIH:jbNKhG1aJR`dGaboE7[UaofCD7lIHSm264Mi`RCQLHPhSe664)hbCQf7f(4iOW]?gbNGH[Xo*UiOXbd_di*Qm)D9OS])G`oCU)7de|_]ZQ;hjYnodon;ATB78FXH**^?eZ0fEZFF5(VP?=8;H)aTbB6n8b)3UV4Fbi1AiT22`G|H1Q[1NoCTPFM*RU*5NU|b5bS0cF`(Z0kc1]9To^bXJOHcLa4aiI1fBOWg2T[Q2C0)0EB:Y)ejVm5Yih;X`li612VSTR0NV?X1Z47DRJT3B:dh:CYZE8:T3B*(DHbMi2jAQBgP9(^iZTkJOToM0l*8D|8HX]`L=D)d68]1lMd`_^8Zj_2YVa9GU|A(6=2m1D`WF1m2BDMF:^fT)jQ9dhdPUG;M6?`g=o5Q6A2N(R15l]7PIQ|[`j`gO2Z=YCYYa()iH=:a(a6O0D1GBbiK9BCMYTF0b6hE8MRf=N1(RUkh1YX|JAB`BKH9ZjXR|HmbPY(|Bll(*ld68FOjHl__346_GfMPS`iL*nBIWc4HaY_cJbfh)OLVFdR|Obo;d]Yk31RU^hX=XjbUXD=AA|eC0MG|OF6I9^]8B`FCFoTBbS8WZ)Y]X=]j9HA^CA7a9c2HV|A`Tk8B14;fkAD0Ob]k5YMS=8c*7Y]|P4;e;BL*mI7Vk*;11110mFnmZ17La]BKUF]|Jjf?I*|(GAQc4XNh0=NFj3MW[R[|Pfmd7MdG:1TP)g(UX06n9^b=URoSNP;|VKH_HJ81TQ`(DoiabefAk`H1Ri`?`XQBMXi_?YT9oDi[F]KLkk[9|6nU^b`je;KVMgn=7YPQMfJ72ma[E)LT:3_F]n?9F=dG)c]o1FaF^|Ui_oGo[KSjbJXbX_(FaM5QiZg6JkekN6[TZaZZ:Ff_|[77?JRn^CBighgnJ1K*UPeE_e^|l43(lCf8FhAn*P4)6:_Nil?ckfMN?FPL3)_Wm`fA]D0?)0dnN]H6N)^MEMOAnm;1i|clDeKLJahRcl[4hUCFfR3OUTo|fEV|Be3`DeKkhmJVD_UZRT9hnNDC5Yem?EN6aI2_NNidJd)T1WCWC5Do8P1hSl4AKmh^Oc1jP;9c|T::A:ZZN^bJefa]BJ)nY:*Pj;nhf^1WI|G[6;jEinOGTik=n`Dbh2En|kmKWO[RKkVM0`6Fhj)IW5abUkHME*6eKIWU0hKHo[CoNc;LY6MlXNYJWFDkOEfmNMgU07lJ_:;k]7X9Xn[KKhW(GC)U=a]?M8_QQbY`Jj`8cM0|0bJ4C=4iTgFgaZ3TOn^o2K?51bkJA)go_m8KEo*LMF:Dk.mmf

     

    Fonction Inverse f(x) = 1 MMF.7h]`3`00QEO=L]]637h2_h))m0b]FN`?^La=EQUGDd_bB8cCPbm|b[ZJfU9::fdBSmnm`)jB11EB]F`;7k0;h(=R8NYQ|GZogRaWaF:m^WRmN9Q_lUVagTC;l_SW|WcLOI[LEOG;HElnCCk^mY=ok5C:bh^7HU7LiU7nmiOb^3_|[`1EmoUVRdhR4dnBN29*lm)|b2)0N6;SRAB0FPW_Y7ZWbISoNWLkFjbRbh^gRhM]GQB;e*dU|=f^I||ln_1BeI=]MCc^mXnhn^DHRGRiW5OkhiOjfj[jedM0=*b[iHUJN[GZe)^WgfoZZ_Z[]NTQFg1WC]b1EbO3`M)hf3eG;a?DCCJ7ig;OFV`l?gbYMlR=[lm6el(Hja7J((8KcQ67LlaQQ3Z(L8MalS3(7|KYbe?j8KPL)oDAn_8LOGV)_QbQ;dOXbg7jLYRn7:N_ATiOSM1GYoBMoS]N7AV3m3;449^PAff|S9LEbZ03d0SB|(R***I3*XHPYlbCYDE901T26fA|H8Smk|lAbL:;U0H4FK8UU8JIFPlX3*P6ddKnk;9Xm2Ub4e(ET7E8Q_dI2n8B(*d0UXVTjPBI`V|EP:_2=7P6BZ2A4njHjP2Z*EB9Y05I;cTY)6VFPZ*:I0e*S9gT9I26KN4Yb;C;CMYnC5h3aA=*`0ZRg1Td*;D7R43cdc4mib[YhZZD4ENFnlhHd3`5CBWHh41;AUD[_Tach5?*cD9:hJXeQViXn|Lb8SYSA8cP[LGC(9A6f6ohDAQ=OM:dPg7GXV5U4]h3Q[:**KI(c[Y)B`BCFB|T|R]Y`X^*^?0=(9gG966Nj11DTdMR7N(6IEfDU5n6U3M2b^:W53mLQUBkbZH16Kj5b3LaDmJ::LGG*GIm65:f55h5GiJ7]kh?6jBhRCNRmEg*X:BSIRV1ZgHNF6K9^]*b`FAFoTbbR9WZ:Y]Ye]jIH*NC9Ga;bSXV|aaTk8J14;gI8Z0?IFm`:CIiQ)K0M0L4XSNDA=Y3UYL;16]40=6cmDHS^(7DVY*[KF_dek:5QVm()4QSg*4ZbUG[|ULE=b3Kd`Lg8VD390O^ISB0UlC=B=TROSKPaZA]4F|=T)abP):ODfi(]P(65;|OP8=BM0]MOcHIQTUYfZFmdg73|RfTViHMJT]b(k_3Sd`A^kASQNlNnIQT1HOjEW`5Zn|RInO_4:`:MmVP]n6oMI)?[1XmZV1a;1eF`FZLiXMG|2H^Rk6|d]JJ)V_J|mZcNk?ceOROHP4MbF3FVoFjR(*Dki)H9_P7962CXLYm;ScoLO;e`n]P*2MoO9Sd1SF`N)39da_XZG=FehN`SQhf[gOk|_kVLHYhECfFalYSRgQC?KT_HejCXNJn[7OUKdnE3=TBQOch:B1:?_mj[(^09M_a?^SDP4h?j(b9[Wa21_*HPCOJ^UolI0h0IN5TQaBeE5WgUV]B^k(QQ*h[=CW1aO?K3Ak6jU0ohgOBX_Yj3?gYGc0E[|?Wjm_ejCXlCOLc8)0fg7CmRg))d_K3(Z:b;EI5A)jf?jloG|nf)AWOb?^Zb5L5OEnmOWdXX^CbUHAiY2kO_21A^(MW^L^g=mc`7k86FS`.mmf

    Qu’est-ce donc que cette forme géométrique ?

    Le ⨁ au dénominateur représente un terme plus ou moins complexe qui dépend bien évidemment de x.

    Pour f(x) = 1 x²(x-2) MMF.7h]`3`00QEO=L]]637h2_h))m0b]FN`?^La=EQUGDd_bB8cCPbm|b[ZJfU9::fdBSmnm`)jB11EB]F`;7k0;h(=R8NYQ|GZogRaWaF:m^WRmN9Q_lUVagTC;l_SW|WcLOI[LEOG;HElnCCk^mY=ok5C:bh^7HU7LiU7nmiOb^3_|[`1EmoUVRdhR4dnBN29*lm)|b2)0N6;SRAB0FPW_Y7ZWbISoNWLkFjbRbh^gRhM]GQB;e*dU|=f^I||ln_1BeI=]MCc^mXnhn^DHRGRiW5OkhiOjfj[jedM0=*b[iHUJN[GZe)^WgfoZZ_Z[]NTQFg1WC]b1EbO3`M)hf3eG;a?DCCJ7ig;OFV`l?gbYMlR=[lm6el(Hja7J((8KcQ67LlaQQ3Z(L8MalS3(7|KYbe?j8KPL)oDAn_8LOGV)_QbQ;dOXbg7jLYRn7:N_ATiOSM1GYoBMoS]N7AV3m3;449^PAff|S9LEbZ03d0SB|(R***I3*XHPYlbCYDE901T26fA|H8Smk|lAbL:;U0H4FK8UU8JIFPlX3*P6ddKnk;9Xm2Ub4e(ET7E8Q_dI2n8B(*d0UXVTjPBI`V|EP:_2=7P6BZ2A4njHjP2Z*EB9Y05I;cTY)6VFPZ*:I0e*S9gT9I26KN4Yb;C;CMYnC5h3aA=*`0ZRg1Td*;D7R43cdc4mib[YhZZD4ENFnlhHd3`5CBWHh41;AUD[_Tach5?*cD9:hJXeQViXn|Lb8SYSA8cP[LGC(9A6f6ohDAQ=OM:dPg7GXV5U4]h3Q[:**KI(c[Y)B`BCFB|T|R]Y`X^*^?0=(9gG966Nj11DTdMR7N(6IEfDU5n6U3M2b^:W53mLQUBkbZH16Kj5b3LaDmJ::LGG*GIm65:f55h5GiJ7]kh?6jBhRCNRmEg*X:BSIRV1ZgHNF6K9^]*b`FAFoTbbR9WZ:Y]Ye]jIH*NC9Ga;bSXV|aaTk8J14;gI8Z0?IFm`:CIiQ)K0M0L4XSNDA=Y3UYL;16]40=6cmDHS^(7DVY*[KF_dek:5QVm()4QSg*4ZbUG[|ULE=b3Kd`Lg8VD390O^ISB0UlC=B=TROSKPaZA]4F|=T)abP):ODfi(]P(65;|OP8=BM0]MOcHIQTUYfZFmdg73|RfTViHMJT]b(k_3Sd`A^kASQNlNnIQT1HOjEW`5Zn|RInO_4:`:MmVP]n6oMI)?[1XmZV1a;1eF`FZLiXMG|2H^Rk6|d]JJ)V_J|mZcNk?ceOROHP4MbF3FVoFjR(*Dki)H9_P7962CXLYm;ScoLO;e`n]P*2MoO9Sd1SF`N)39da_XZG=FehN`SQhf[gOk|_kVLHYhECfFalYSRgQC?KT_HejCXNJn[7OUKdnE3=TBQOch:B1:?_mj[(^09M_a?^SDP4h?j(b9[Wa21_*HPCOJ^UolI0h0IN5TQaBeE5WgUV]B^k(QQ*h[=CW1aO?K3Ak6jU0ohgOBX_Yj3?gYGc0E[|?Wjm_ejCXlCOLc8)0fg7CmRg))d_K3(Z:b;EI5A)jf?jloG|nf)AWOb?^Zb5L5OEnmOWdXX^CbUHAiY2kO_21A^(MW^L^g=mc`7k86FS`.mmf , nous avons ⨁ = x² ( x - 2 )

    Quelle contrainte impose la fonction ?

    Tout ce qui est au dénominateur ne doit jamais s'annuler, nous avons donc ⨁ ≠ 0. Nous obtenons alors le domaine de définition Df = MMF.7h]V3`00QEM]Lm|f3?h5oPonZ=`Y?X8_4]E_SZMV_|EbcUKKgLgkX6EZjY]ONXZj]N_U_hlP:*Ub9Bm)HS`02N01*ESN;K)gjleZWRoGfNCkI;OHY?=l_*UFAOeYECc_WjJ?IOEb?QF7jHOmJOZgWW5n(mWUbo`Q3CiFaE)m?imVWn[S`FSOYi^]lA)XL1Z5DfHd?lgc=008YcZLLPI6bn4=Smi`=:Jo?Sk(UeU`(gVMk;IYWRncNlaQ^lgVZcAhme9FdfeIeo_C|eWmDPL|G:dFiJWnDWg;bWmL1:)6HCFoD7)W5YejOOSc_R[;_eZK7;9iMn[27CQe=1`l3_?m|GbI6]edLchFYmJR`lGiBkDgg)SjI7*mS;4NX*dS_)4JLKS674JX``Qg62L?`naQW3joY)n3lk5C7j7?[m7WenSc4OYlQ3hOYln7jO=anV;Tm(D8OG59gn[o=EN7Ql2M3264b^^==QC:bL;883f*1|AnTD83mhH83Ej)RBN=Rb8?4P)dUdd3*nQfO`i*ITk4=(3;W2c1==A()h1YP3NX=_9WVdFSS`dg=Q(NJH^hgin*83HAe*0PVG2|SYLa_1*Nf2[(_6O011XiXXja3R0JQ9F86Y3dT^)(TRHYL:a0dP11f75J0Zk85YX2Sk_L^)k7Y3D*=041Y232WT43A7^01TQj)Z[WG4AMG14ChT9Cg`T1TZHP(*G]7DQ)Z4Y1UdT:G0ZbFHPYg;I6g`e=ofQ2A2J4R6:d]FPJ2]?`naDm2RFaCiYfD?IJ=:aDA7]0HAKLbi[8BMMY4B(bJHF8MbF=J14R6kh1Z_(JAL*C7X9XlXRdIMbPY8|Bdl|*ddJ8BO`Hho_;44]KfMPSAKLPnBIVC5Xaa_SBbkH?OLXJ``__Bm?`f_EQP`*edDKD[P|J57GD=2I`flh3CBa9Ue[2R4c:Wg0B(A5MIA=9fS]Ai62BR6j9BLLTVX:4g31P[3MK6?*Qk`d^*BH?TaBXkX20mHHBRg]8dg818hd8`7ZfgVP4)iQJTk2UKHg^F[I*dHdA1G4X)h15^FeMmZYR1fAknV1796l0Yl3NS0K*T]PIbE]4c`K|V=*]8Zd1W5`)4?AcbXk9M|208?L3c:1TgD;KWdf6OU:ZMVW_M)b`K0]YYfF7fY;Lcao=AbH;KMZQ()l)^IQX1H_jE_?bE]]5eTkO`E^5fJFmG__ofThn]4[SDGR;IFVal5IU=Cnl_3FbFHaU5KOFf5[SWUEOgI]L[lKo50_`B0JcgZcGNL1ViSjaFFCn00GCI4IU?aN)7bnnOSPM3)ShS`nCcR065PllNCX3?WG)Zn[|en73i]gnE5CO78h=c|[WXRhMePI_bT)1glNL9S6JmdFe;ohhU=aWRaCBn|TSC3kmFUN5aic|N)]eHT0W1gCZ*ULL30=lS30gF]]OllW|PI6IUBdBf595eE|^DFg?1QGB[iCXa2aN?6c(HFCWjVRnU^KUem[gYg_1S=T)Gj`OeYO[c6WJW`71K3)KkWjacXfdOKL:|6c;;0o*gOKWmHNknCI5hb]jco8dbo7kj]gggN:g((B(kLo_`NKVeJci3fXO=AD.mmf \ { solution(s) de ⨁ = 0 }

    Exemple : f(x) = 1 (x-1)(2x+4) MMF.7h]`3`00QEO=L]]637h2_h))m0b]FN`?^La=EQUGDd_bB8cCPbm|b[ZJfU9::fdBSmnm`)jB11EB]F`;7k0;h(=R8NYQ|GZogRaWaF:m^WRmN9Q_lUVagTC;l_SW|WcLOI[LEOG;HElnCCk^mY=ok5C:bh^7HU7LiU7nmiOb^3_|[`1EmoUVRdhR4dnBN29*lm)|b2)0N6;SRAB0FPW_Y7ZWbISoNWLkFjbRbh^gRhM]GQB;e*dU|=f^I||ln_1BeI=]MCc^mXnhn^DHRGRiW5OkhiOjfj[jedM0=*b[iHUJN[GZe)^WgfoZZ_Z[]NTQFg1WC]b1EbO3`M)hf3eG;a?DCCJ7ig;OFV`l?gbYMlR=[lm6el(Hja7J((8KcQ67LlaQQ3Z(L8MalS3(7|KYbe?j8KPL)oDAn_8LOGV)_QbQ;dOXbg7jLYRn7:N_ATiOSM1GYoBMoS]N7AV3m3;449^PAff|S9LEbZ03d0SB|(R***I3*XHPYlbCYDE901T26fA|H8Smk|lAbL:;U0H4FK8UU8JIFPlX3*P6ddKnk;9Xm2Ub4e(ET7E8Q_dI2n8B(*d0UXVTjPBI`V|EP:_2=7P6BZ2A4njHjP2Z*EB9Y05I;cTY)6VFPZ*:I0e*S9gT9I26KN4Yb;C;CMYnC5h3aA=*`0ZRg1Td*;D7R43cdc4mib[YhZZD4ENFnlhHd3`5CBWHh41;AUD[_Tach5?*cD9:hJXeQViXn|Lb8SYSA8cP[LGC(9A6f6ohDAQ=OM:dPg7GXV5U4]h3Q[:**KI(c[Y)B`BCFB|T|R]Y`X^*^?0=(9gG966Nj11DTdMR7N(6IEfDU5n6U3M2b^:W53mLQUBkbZH16Kj5b3LaDmJ::LGG*GIm65:f55h5GiJ7]kh?6jBhRCNRmEg*X:BSIRV1ZgHNF6K9^]*b`FAFoTbbR9WZ:Y]Ye]jIH*NC9Ga;bSXV|aaTk8J14;gI8Z0?IFm`:CIiQ)K0M0L4XSNDA=Y3UYL;16]40=6cmDHS^(7DVY*[KF_dek:5QVm()4QSg*4ZbUG[|ULE=b3Kd`Lg8VD390O^ISB0UlC=B=TROSKPaZA]4F|=T)abP):ODfi(]P(65;|OP8=BM0]MOcHIQTUYfZFmdg73|RfTViHMJT]b(k_3Sd`A^kASQNlNnIQT1HOjEW`5Zn|RInO_4:`:MmVP]n6oMI)?[1XmZV1a;1eF`FZLiXMG|2H^Rk6|d]JJ)V_J|mZcNk?ceOROHP4MbF3FVoFjR(*Dki)H9_P7962CXLYm;ScoLO;e`n]P*2MoO9Sd1SF`N)39da_XZG=FehN`SQhf[gOk|_kVLHYhECfFalYSRgQC?KT_HejCXNJn[7OUKdnE3=TBQOch:B1:?_mj[(^09M_a?^SDP4h?j(b9[Wa21_*HPCOJ^UolI0h0IN5TQaBeE5WgUV]B^k(QQ*h[=CW1aO?K3Ak6jU0ohgOBX_Yj3?gYGc0E[|?Wjm_ejCXlCOLc8)0fg7CmRg))d_K3(Z:b;EI5A)jf?jloG|nf)AWOb?^Zb5L5OEnmOWdXX^CbUHAiY2kO_21A^(MW^L^g=mc`7k86FS`.mmf

    Ici, ⨁ = ( x - 1 )( 2x + 4 ). On résout ( x - 1 )( 2x + 4 ) = 0 ⇔ x - 1 = 0  ou  2x + 4 = 0 ⇔ x = 1  ou  x = -2. Les racines du dénominateur sont donc 1 et -2. Ainsi Df = MMF.7h]V3`00QEM]Lm|f3?h5oPonZ=`Y?X8_4]E_SZMV_|EbcUKKgLgkX6EZjY]ONXZj]N_U_hlP:*Ub9Bm)HS`02N01*ESN;K)gjleZWRoGfNCkI;OHY?=l_*UFAOeYECc_WjJ?IOEb?QF7jHOmJOZgWW5n(mWUbo`Q3CiFaE)m?imVWn[S`FSOYi^]lA)XL1Z5DfHd?lgc=008YcZLLPI6bn4=Smi`=:Jo?Sk(UeU`(gVMk;IYWRncNlaQ^lgVZcAhme9FdfeIeo_C|eWmDPL|G:dFiJWnDWg;bWmL1:)6HCFoD7)W5YejOOSc_R[;_eZK7;9iMn[27CQe=1`l3_?m|GbI6]edLchFYmJR`lGiBkDgg)SjI7*mS;4NX*dS_)4JLKS674JX``Qg62L?`naQW3joY)n3lk5C7j7?[m7WenSc4OYlQ3hOYln7jO=anV;Tm(D8OG59gn[o=EN7Ql2M3264b^^==QC:bL;883f*1|AnTD83mhH83Ej)RBN=Rb8?4P)dUdd3*nQfO`i*ITk4=(3;W2c1==A()h1YP3NX=_9WVdFSS`dg=Q(NJH^hgin*83HAe*0PVG2|SYLa_1*Nf2[(_6O011XiXXja3R0JQ9F86Y3dT^)(TRHYL:a0dP11f75J0Zk85YX2Sk_L^)k7Y3D*=041Y232WT43A7^01TQj)Z[WG4AMG14ChT9Cg`T1TZHP(*G]7DQ)Z4Y1UdT:G0ZbFHPYg;I6g`e=ofQ2A2J4R6:d]FPJ2]?`naDm2RFaCiYfD?IJ=:aDA7]0HAKLbi[8BMMY4B(bJHF8MbF=J14R6kh1Z_(JAL*C7X9XlXRdIMbPY8|Bdl|*ddJ8BO`Hho_;44]KfMPSAKLPnBIVC5Xaa_SBbkH?OLXJ``__Bm?`f_EQP`*edDKD[P|J57GD=2I`flh3CBa9Ue[2R4c:Wg0B(A5MIA=9fS]Ai62BR6j9BLLTVX:4g31P[3MK6?*Qk`d^*BH?TaBXkX20mHHBRg]8dg818hd8`7ZfgVP4)iQJTk2UKHg^F[I*dHdA1G4X)h15^FeMmZYR1fAknV1796l0Yl3NS0K*T]PIbE]4c`K|V=*]8Zd1W5`)4?AcbXk9M|208?L3c:1TgD;KWdf6OU:ZMVW_M)b`K0]YYfF7fY;Lcao=AbH;KMZQ()l)^IQX1H_jE_?bE]]5eTkO`E^5fJFmG__ofThn]4[SDGR;IFVal5IU=Cnl_3FbFHaU5KOFf5[SWUEOgI]L[lKo50_`B0JcgZcGNL1ViSjaFFCn00GCI4IU?aN)7bnnOSPM3)ShS`nCcR065PllNCX3?WG)Zn[|en73i]gnE5CO78h=c|[WXRhMePI_bT)1glNL9S6JmdFe;ohhU=aWRaCBn|TSC3kmFUN5aic|N)]eHT0W1gCZ*ULL30=lS30gF]]OllW|PI6IUBdBf595eE|^DFg?1QGB[iCXa2aN?6c(HFCWjVRnU^KUem[gYg_1S=T)Gj`OeYO[c6WJW`71K3)KkWjacXfdOKL:|6c;;0o*gOKWmHNknCI5hb]jco8dbo7kj]gggN:g((B(kLo_`NKVeJci3fXO=AD.mmf \ { -2; 1 }.

     

    Autres Fonctions f(x) = ⊚

     

    Qu’est-ce donc que cette forme géométrique ?

    Le ⊚ au numérateur représente un terme plus ou moins complexe qui dépend bien évidemment de x.

    Pour f(x) = ( x + 4 )( x² - 2 ), nous avons tout simplement ⊚ = ( x + 4 )( x² - 2 )

    Quelle contrainte impose la fonction ?

    Cette fonction représente en fait toutes les fonctions ne correspondant pas aux 3 cas précédents. Cette fonction n'est pas identifiable à une fonction inverse, racine carrée ou logarithmique. Dans ce cas, aucune contrainte n'est imposée à x. Ainsi son domaine de définition sera l'ensemble des réels, Df = MMF.7h]V3`00QEM]Lm|f3?h5oPonZ=`Y?X8_4]E_SZMV_|EbcUKKgLgkX6EZjY]ONXZj]N_U_hlP:*Ub9Bm)HS`02N01*ESN;K)gjleZWRoGfNCkI;OHY?=l_*UFAOeYECc_WjJ?IOEb?QF7jHOmJOZgWW5n(mWUbo`Q3CiFaE)m?imVWn[S`FSOYi^]lA)XL1Z5DfHd?lgc=008YcZLLPI6bn4=Smi`=:Jo?Sk(UeU`(gVMk;IYWRncNlaQ^lgVZcAhme9FdfeIeo_C|eWmDPL|G:dFiJWnDWg;bWmL1:)6HCFoD7)W5YejOOSc_R[;_eZK7;9iMn[27CQe=1`l3_?m|GbI6]edLchFYmJR`lGiBkDgg)SjI7*mS;4NX*dS_)4JLKS674JX``Qg62L?`naQW3joY)n3lk5C7j7?[m7WenSc4OYlQ3hOYln7jO=anV;Tm(D8OG59gn[o=EN7Ql2M3264b^^==QC:bL;883f*1|AnTD83mhH83Ej)RBN=Rb8?4P)dUdd3*nQfO`i*ITk4=(3;W2c1==A()h1YP3NX=_9WVdFSS`dg=Q(NJH^hgin*83HAe*0PVG2|SYLa_1*Nf2[(_6O011XiXXja3R0JQ9F86Y3dT^)(TRHYL:a0dP11f75J0Zk85YX2Sk_L^)k7Y3D*=041Y232WT43A7^01TQj)Z[WG4AMG14ChT9Cg`T1TZHP(*G]7DQ)Z4Y1UdT:G0ZbFHPYg;I6g`e=ofQ2A2J4R6:d]FPJ2]?`naDm2RFaCiYfD?IJ=:aDA7]0HAKLbi[8BMMY4B(bJHF8MbF=J14R6kh1Z_(JAL*C7X9XlXRdIMbPY8|Bdl|*ddJ8BO`Hho_;44]KfMPSAKLPnBIVC5Xaa_SBbkH?OLXJ``__Bm?`f_EQP`*edDKD[P|J57GD=2I`flh3CBa9Ue[2R4c:Wg0B(A5MIA=9fS]Ai62BR6j9BLLTVX:4g31P[3MK6?*Qk`d^*BH?TaBXkX20mHHBRg]8dg818hd8`7ZfgVP4)iQJTk2UKHg^F[I*dHdA1G4X)h15^FeMmZYR1fAknV1796l0Yl3NS0K*T]PIbE]4c`K|V=*]8Zd1W5`)4?AcbXk9M|208?L3c:1TgD;KWdf6OU:ZMVW_M)b`K0]YYfF7fY;Lcao=AbH;KMZQ()l)^IQX1H_jE_?bE]]5eTkO`E^5fJFmG__ofThn]4[SDGR;IFVal5IU=Cnl_3FbFHaU5KOFf5[SWUEOgI]L[lKo50_`B0JcgZcGNL1ViSjaFFCn00GCI4IU?aN)7bnnOSPM3)ShS`nCcR065PllNCX3?WG)Zn[|en73i]gnE5CO78h=c|[WXRhMePI_bT)1glNL9S6JmdFe;ohhU=aWRaCBn|TSC3kmFUN5aic|N)]eHT0W1gCZ*ULL30=lS30gF]]OllW|PI6IUBdBf595eE|^DFg?1QGB[iCXa2aN?6c(HFCWjVRnU^KUem[gYg_1S=T)Gj`OeYO[c6WJW`71K3)KkWjacXfdOKL:|6c;;0o*gOKWmHNknCI5hb]jco8dbo7kj]gggN:g((B(kLo_`NKVeJci3fXO=AD.mmf .

    Exemple : f(x) = (x + 1)² + 4x + 5

    Ici, ⊚ = (x + 1)² + 4x + 5, nous identifions aucun des cas précédents. C'est pourquoi Df = MMF.7h]V3`00QEM]Lm|f3?h5oPonZ=`Y?X8_4]E_SZMV_|EbcUKKgLgkX6EZjY]ONXZj]N_U_hlP:*Ub9Bm)HS`02N01*ESN;K)gjleZWRoGfNCkI;OHY?=l_*UFAOeYECc_WjJ?IOEb?QF7jHOmJOZgWW5n(mWUbo`Q3CiFaE)m?imVWn[S`FSOYi^]lA)XL1Z5DfHd?lgc=008YcZLLPI6bn4=Smi`=:Jo?Sk(UeU`(gVMk;IYWRncNlaQ^lgVZcAhme9FdfeIeo_C|eWmDPL|G:dFiJWnDWg;bWmL1:)6HCFoD7)W5YejOOSc_R[;_eZK7;9iMn[27CQe=1`l3_?m|GbI6]edLchFYmJR`lGiBkDgg)SjI7*mS;4NX*dS_)4JLKS674JX``Qg62L?`naQW3joY)n3lk5C7j7?[m7WenSc4OYlQ3hOYln7jO=anV;Tm(D8OG59gn[o=EN7Ql2M3264b^^==QC:bL;883f*1|AnTD83mhH83Ej)RBN=Rb8?4P)dUdd3*nQfO`i*ITk4=(3;W2c1==A()h1YP3NX=_9WVdFSS`dg=Q(NJH^hgin*83HAe*0PVG2|SYLa_1*Nf2[(_6O011XiXXja3R0JQ9F86Y3dT^)(TRHYL:a0dP11f75J0Zk85YX2Sk_L^)k7Y3D*=041Y232WT43A7^01TQj)Z[WG4AMG14ChT9Cg`T1TZHP(*G]7DQ)Z4Y1UdT:G0ZbFHPYg;I6g`e=ofQ2A2J4R6:d]FPJ2]?`naDm2RFaCiYfD?IJ=:aDA7]0HAKLbi[8BMMY4B(bJHF8MbF=J14R6kh1Z_(JAL*C7X9XlXRdIMbPY8|Bdl|*ddJ8BO`Hho_;44]KfMPSAKLPnBIVC5Xaa_SBbkH?OLXJ``__Bm?`f_EQP`*edDKD[P|J57GD=2I`flh3CBa9Ue[2R4c:Wg0B(A5MIA=9fS]Ai62BR6j9BLLTVX:4g31P[3MK6?*Qk`d^*BH?TaBXkX20mHHBRg]8dg818hd8`7ZfgVP4)iQJTk2UKHg^F[I*dHdA1G4X)h15^FeMmZYR1fAknV1796l0Yl3NS0K*T]PIbE]4c`K|V=*]8Zd1W5`)4?AcbXk9M|208?L3c:1TgD;KWdf6OU:ZMVW_M)b`K0]YYfF7fY;Lcao=AbH;KMZQ()l)^IQX1H_jE_?bE]]5eTkO`E^5fJFmG__ofThn]4[SDGR;IFVal5IU=Cnl_3FbFHaU5KOFf5[SWUEOgI]L[lKo50_`B0JcgZcGNL1ViSjaFFCn00GCI4IU?aN)7bnnOSPM3)ShS`nCcR065PllNCX3?WG)Zn[|en73i]gnE5CO78h=c|[WXRhMePI_bT)1glNL9S6JmdFe;ohhU=aWRaCBn|TSC3kmFUN5aic|N)]eHT0W1gCZ*ULL30=lS30gF]]OllW|PI6IUBdBf595eE|^DFg?1QGB[iCXa2aN?6c(HFCWjVRnU^KUem[gYg_1S=T)Gj`OeYO[c6WJW`71K3)KkWjacXfdOKL:|6c;;0o*gOKWmHNknCI5hb]jco8dbo7kj]gggN:g((B(kLo_`NKVeJci3fXO=AD.mmf .

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    ↬ Certaines fonctions correspondent à un mixte de cas, il faudra alors prendre en compte les contraintes de chacun des cas. Par exemple, pour f(x) = 1 x-1 MMF.7h]`3`00QEO=L]]637h2_h))m0b]FN`?^La=EQUGDd_bB8cCPbm|b[ZJfU9::fdBSmnm`)jB11EB]F`;7k0;h(=R8NYQ|GZogRaWaF:m^WRmN9Q_lUVagTC;l_SW|WcLOI[LEOG;HElnCCk^mY=ok5C:bh^7HU7LiU7nmiOb^3_|[`1EmoUVRdhR4dnBN29*lm)|b2)0N6;SRAB0FPW_Y7ZWbISoNWLkFjbRbh^gRhM]GQB;e*dU|=f^I||ln_1BeI=]MCc^mXnhn^DHRGRiW5OkhiOjfj[jedM0=*b[iHUJN[GZe)^WgfoZZ_Z[]NTQFg1WC]b1EbO3`M)hf3eG;a?DCCJ7ig;OFV`l?gbYMlR=[lm6el(Hja7J((8KcQ67LlaQQ3Z(L8MalS3(7|KYbe?j8KPL)oDAn_8LOGV)_QbQ;dOXbg7jLYRn7:N_ATiOSM1GYoBMoS]N7AV3m3;449^PAff|S9LEbZ03d0SB|(R***I3*XHPYlbCYDE901T26fA|H8Smk|lAbL:;U0H4FK8UU8JIFPlX3*P6ddKnk;9Xm2Ub4e(ET7E8Q_dI2n8B(*d0UXVTjPBI`V|EP:_2=7P6BZ2A4njHjP2Z*EB9Y05I;cTY)6VFPZ*:I0e*S9gT9I26KN4Yb;C;CMYnC5h3aA=*`0ZRg1Td*;D7R43cdc4mib[YhZZD4ENFnlhHd3`5CBWHh41;AUD[_Tach5?*cD9:hJXeQViXn|Lb8SYSA8cP[LGC(9A6f6ohDAQ=OM:dPg7GXV5U4]h3Q[:**KI(c[Y)B`BCFB|T|R]Y`X^*^?0=(9gG966Nj11DTdMR7N(6IEfDU5n6U3M2b^:W53mLQUBkbZH16Kj5b3LaDmJ::LGG*GIm65:f55h5GiJ7]kh?6jBhRCNRmEg*X:BSIRV1ZgHNF6K9^]*b`FAFoTbbR9WZ:Y]Ye]jIH*NC9Ga;bSXV|aaTk8J14;gI8Z0?IFm`:CIiQ)K0M0L4XSNDA=Y3UYL;16]40=6cmDHS^(7DVY*[KF_dek:5QVm()4QSg*4ZbUG[|ULE=b3Kd`Lg8VD390O^ISB0UlC=B=TROSKPaZA]4F|=T)abP):ODfi(]P(65;|OP8=BM0]MOcHIQTUYfZFmdg73|RfTViHMJT]b(k_3Sd`A^kASQNlNnIQT1HOjEW`5Zn|RInO_4:`:MmVP]n6oMI)?[1XmZV1a;1eF`FZLiXMG|2H^Rk6|d]JJ)V_J|mZcNk?ceOROHP4MbF3FVoFjR(*Dki)H9_P7962CXLYm;ScoLO;e`n]P*2MoO9Sd1SF`N)39da_XZG=FehN`SQhf[gOk|_kVLHYhECfFalYSRgQC?KT_HejCXNJn[7OUKdnE3=TBQOch:B1:?_mj[(^09M_a?^SDP4h?j(b9[Wa21_*HPCOJ^UolI0h0IN5TQaBeE5WgUV]B^k(QQ*h[=CW1aO?K3Ak6jU0ohgOBX_Yj3?gYGc0E[|?Wjm_ejCXlCOLc8)0fg7CmRg))d_K3(Z:b;EI5A)jf?jloG|nf)AWOb?^Zb5L5OEnmOWdXX^CbUHAiY2kO_21A^(MW^L^g=mc`7k86FS`.mmf , nous devons avoir x - 1 ≥ 0 (contrainte de la racine) et x - 1 ≠ 0 (contrainte de l'inverse). Ainsi en regroupant ces 2 contraintes, nous obtenons x - 1 > 0 , d'où Df = 1 ; + MMF.7h_N3`00QEMOLn963?l4n*hlVQV7FNdONgem8]BG(PdV0kiL7gQa[fk:=86[`kEgcNBkEeZ_KIVcJDR2OY9FdTn[GLa^VKeOKeKcO;W)[Uj_MX]=)|oGVf1EW?iH5HokCi?k|WXi7XZWbLOmHO:gWDTi_M[Ubo`^3M:o_QBWoO5`3JQjB3MK31:HL1:54h6J7nMi6P244jW`C`2Z8GjWTWMBXcGmiOi^_|b2jMGKeFjKi_Tb^jD:]]]|_TZ33bmU=MVFYm?nl8SN;jM0Q:_EXSbL_UCO|_:O)PFZHEP]cmBbEZ])_GkjkKHZbcmKVajbnG3V;1cDjVPhNAcVnnObIH:jbNKhG1aJR`dGaboE7[UaofCD7lIHSm264Mi`RCQLHPhSe664)hbCQf7f(4iOW]?gbNGH[Xo*UiOXbd_di*Qm)D9OS])G`oCU)7de|_]ZQ;hjYnodon;ATB78FXH**^?eZ0fEZFF5(VP?=8;H)aTbB6n8b)3UV4Fbi1AiT22`G|H1Q[1NoCTPFM*RU*5NU|b5bS0cF`(Z0kc1]9To^bXJOHcLa4aiI1fBOWg2T[Q2C0)0EB:Y)ejVm5Yih;X`li612VSTR0NV?X1Z47DRJT3B:dh:CYZE8:T3B*(DHbMi2jAQBgP9(^iZTkJOToM0l*8D|8HX]`L=D)d68]1lMd`_^8Zj_2YVa9GU|A(6=2m1D`WF1m2BDMF:^fT)jQ9dhdPUG;M6?`g=o5Q6A2N(R15l]7PIQ|[`j`gO2Z=YCYYa()iH=:a(a6O0D1GBbiK9BCMYTF0b6hE8MRf=N1(RUkh1YX|JAB`BKH9ZjXR|HmbPY(|Bll(*ld68FOjHl__346_GfMPS`iL*nBIWc4HaY_cJbfh)OLVFdR|Obo;d]Yk31RU^hX=XjbUXD=AA|eC0MG|OF6I9^]8B`FCFoTBbS8WZ)Y]X=]j9HA^CA7a9c2HV|A`Tk8B14;fkAD0Ob]k5YMS=8c*7Y]|P4;e;BL*mI7Vk*;11110mFnmZ17La]BKUF]|Jjf?I*|(GAQc4XNh0=NFj3MW[R[|Pfmd7MdG:1TP)g(UX06n9^b=URoSNP;|VKH_HJ81TQ`(DoiabefAk`H1Ri`?`XQBMXi_?YT9oDi[F]KLkk[9|6nU^b`je;KVMgn=7YPQMfJ72ma[E)LT:3_F]n?9F=dG)c]o1FaF^|Ui_oGo[KSjbJXbX_(FaM5QiZg6JkekN6[TZaZZ:Ff_|[77?JRn^CBighgnJ1K*UPeE_e^|l43(lCf8FhAn*P4)6:_Nil?ckfMN?FPL3)_Wm`fA]D0?)0dnN]H6N)^MEMOAnm;1i|clDeKLJahRcl[4hUCFfR3OUTo|fEV|Be3`DeKkhmJVD_UZRT9hnNDC5Yem?EN6aI2_NNidJd)T1WCWC5Do8P1hSl4AKmh^Oc1jP;9c|T::A:ZZN^bJefa]BJ)nY:*Pj;nhf^1WI|G[6;jEinOGTik=n`Dbh2En|kmKWO[RKkVM0`6Fhj)IW5abUkHME*6eKIWU0hKHo[CoNc;LY6MlXNYJWFDkOEfmNMgU07lJ_:;k]7X9Xn[KKhW(GC)U=a]?M8_QQbY`Jj`8cM0|0bJ4C=4iTgFgaZ3TOn^o2K?51bkJA)go_m8KEo*LMF:Dk.mmf

    ↬ L'énoncé d'un exercice peut vous imposer des contraintes sur x. C'est le cas avec les exercices types géométrique et économique du chapitre polynôme du second degré.

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