Question

If f(g(x))=4x^2-8x and f(x) =x^2-4,then g(x)

Answer 1

We plug in g(x) in to f(x)

f(x) = x^2 - 4
f(g(x)) = 4x^2 - 8x

You plug in g(x) in to f(x) to get f(g(x))

so basically

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

However, we also know that
f(g(x)) = 4x^2 - 8x

so set each equal to each other and solve

g(x)^2 - 4 = 4x^2 - 8x

First add 4 on both sides and then take the square root on both sides. And ta-da!

Answer 2

\[f(g(x))=4x^2-8x\\\qquad\quad=(2x)^2-4(2x)\]