Question

Sabendo que F(g(x))=3x-7 e F(x)= 1/3x-2, então:

Answer 1

Vamos determinar a f(g(x)) e, posteriormente, igualar com o resultado fornecido pelo enunciado.

$Substituindo~"x"~por~g(x)~na~funcao~f(x):\\\\\\\boxed{f(g(x))~=~\frac{1}{3.g(x)}-2}\\\\\\Igualando~com~o~resultado~fornecido:\\\\\\\frac{1}{3.g(x)}-2~=~3x-7\\\\\\Isolando~g(x):\\\\\\\frac{1}{3g(x)}~=~3x-7+2\\\\\\\frac{1}{3g(x)}~=~3x-5\\\\\\1~=~3g(x)~.~(3x-5)\\\\\\3g(x)~=~\frac{1}{3x-5}\\\\\\g(x)~=~\frac{1}{3~.~(3x-5)}\\\\\\\boxed{g(x)~=~\frac{1}{9x-15}}$