Question

let f(x)=x\x-2 find the function y=g(x) so that (fog)(x)=x

Answer 1

You are most likely trying to find the inverse of f(x)=x/x-2 since when inverse functions are composed they equal x or (fog)(x)=x

Answer 2

\(\bf (fog)(x)=x\implies f(\quad g(x)\quad ) = x\\
\textit{only occurs when g(x) is the inverse of f(x), that is}\\ \quad \\p
g(x) = f^{-1}(x)\qquad then\\ \quad \\
f(\quad g(x)\quad ) = x\)

Answer 3

shoot I have a p there :|

Answer 4

\(\bf (fog)(x)=x\implies f(\quad g(x)\quad ) = x\\
\textit{only occurs when g(x) is the inverse of f(x), that is}\\ \quad \\
g(x) = f^{-1}(x)\qquad then\\ \quad \\
f(\quad g(x)\quad ) = x\)

Answer 5

so find the inverse of f(x) and make g(x) THAT

Answer 6

do you want the steps showing how to invert the equation?