Question

(UFBA) sabendo-se que f(g(x))=x³+1 ef-¹(x)=(x-1)/3, determine g(x).

Answer 1

$f(g(x))= x^{3} +1; f^{-1} (x)= \frac{x-1}{3} \\ inverte \ f^{-1}=x \ e \ x=y. =>f^{-1}=\frac{x-1}{3} => x =\frac{y-1}{3}\\ => y =3x +1 =>f (x)= 3x+1 . \\ > f (g (x))= 3g (x)+1 =x^{3}+1 => 3g (x)=x^{3}=> \\ ::g (x)= \frac{x^{3}}{3}$