Question

f(x)= -2^x +4^x/3
x= f(x+1)= -2/3
calcule o valor de x

URGENTE!!!!!

Answer 1

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

$\displaystyle Aplicando~a~f\'{o}rmula~de~Bhaskara~para~2y^{2}-3y+1=0~~e~comparando~com~(a)y^{2}+(b)y+(c)=0,~determinamos~os~coeficientes:~\\a=2{;}~b=-3~e~c=1\\\\C\'alculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(-3)^{2}-4(2)(1)=9-(8)=1\\\\C\'alculo~das~raizes:&\\y^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-3)-\sqrt{1}}{2(2)}=\frac{3-1}{4}=\frac{2}{4}=0,5\\\\y^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-3)+\sqrt{1}}{2(2)}=\frac{3+1}{4}=\frac{4}{4}=1$

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