Question

How would I find f(x) such that (f of g)(x) equals g(x)? I attached the problem in the thing below. Any help would be greatly appreciated, thanks!

Answer 1

f(x) = x^6

Explanation:

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

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The answer to the question in your text is that you want f(x) = x.

Then f(g(x)) = g(x).