The problem in the picture wants you to find f(x) such that (f of g)(x) equals h(x). That's a different question than the one in the statement accompanying the picture.
In h(x), the content of parentheses matches g(x), so we can see that ...
h(x) = g(x)^6
For h(x) = (f of g)(x), this means ...
f(x) = x^6
___
The answer to the question in your text is that you want f(x) = x.
