If $f(g(x))=\sqrt {x^2-2x+8}$ and $f(x)=\sqrt x,$ find $g(x)$.

Question

If $f(g(x))=\sqrt {x^2-2x+8}$ and $f(x)=\sqrt x,$ find $g(x)$.

There is no example like this in my math book.

Answer 1

Maybe it will help you to see what $g(x)$ must be by the following: $$f(g(x)) = \sqrt {g(x)} = \sqrt{x^2 - 2x + 8}$$

Spoiler:

$$g(x) = x^2 - 2x + 8$$

Answer 2

HINT:

$$f(x)=\sqrt x\implies f(x^2-2x+8)=\sqrt{x^2-2x+8}$$