Question

Considerando g(f(x))=-2x+4 e f(x) =x+1, encontre g(x)

Answer 1

$g(x)~=~g\left(\,f\left(\,f^{-1}(x)\,\right)\,\right)$

Vamos então precisar da função inversa de f(x).

$f(x)~=~y~=~x+1\\\\\\Trocando~"x"~por~"y":\\\\\\x~=~y+1\\\\\\Isolando~"y":\\\\\\\boxed{y~=~f^{-1}(x)~=~x-1}$

Podemos agora determinar a g(x):

$g(x)~=~g\left(\,f\left(\,x-1\,\right)\,\right)\\\\\\g(x)~=~-2\,.\,(x-1)~+~4\\\\\\g(x)~=~-2x~+~2~+~4\\\\\\\boxed{g(x)~=~-2x~+~6}$