Given composition of functions find the "inner"

Question

If $f(g(x)) = 4x^2 – 8x$ and $f(x) = x^2 – 4$, then $g(x) = ?$

Answer 1

Hint

You can try this:

$$f(g(x))=[g(x)]^2-4$$

can you finish?

Answer 2

$$f(g(x))=(g(x))^2 - 4 = 4x^2 -4x$$

so

$$g(x)^2 = 4x^2 - 4x + 4 = (2x-2)^2$$

So $g(x)=2x-2$ will work.