function composition and decomposition

Question

let f(x)=x/x-7find a fuction y=g(x) so that (f o g)(x)=x
g(x)=?

Answer 1

The function is f(x)=x/x-7

(f o g)(x)=x

f(g(x))=x

g(x)/(g(x)-7) =x

g(x) =x(g(x)-7)

g(x) =xg(x)-7x

xg(x)-g(x) =7x

g(x) (x-1) =7x

g(x) =7x/(x-1)