Resposta:
S={x∈|R/x= -1 ou x=0}
Explicação passo-a-passo:
f(x)= -2ˣ+4ˣ/3
f(x+1)= -2⁽ˣ⁺¹⁾+4⁽ˣ⁺¹⁾/3= -2/3
-(2ˣ.2¹)+4ˣ.4¹/3= -2/3 ×(3/2)
-3.2ˣ+2.4ˣ= -1
-3.2ˣ+2.(2²)ˣ= -1
-3.2ˣ+2.(2ˣ)²= -1
Chamando 2ˣ=y
-3y+2.y²= -1
2y²-3y+1=0
[tex]\displaystyle Aplicando~a~f\'{o}rmula~de~Bhaskara~para~2y^{2}-3y+1=0~~e~comparando~com~(a)y^{2}+(b)y+(c)=0,~determinamos~os~coeficientes:~\\a=2{;}~b=-3~e~c=1\\\\C\'alculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(-3)^{2}-4(2)(1)=9-(8)=1\\\\C\'alculo~das~raizes:&\\y^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-3)-\sqrt{1}}{2(2)}=\frac{3-1}{4}=\frac{2}{4}=0,5\\\\y^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-3)+\sqrt{1}}{2(2)}=\frac{3+1}{4}=\frac{4}{4}=1[/tex]
Para y=y'=0,5
y=2ˣ=0,5
2ˣ=1/2
2ˣ=2⁻¹
x= -1
para y=y''=1
y=2ˣ=1
2ˣ=1
2ˣ=2⁰
x=0
