<s>[INST] If $f(g(x)) = 4x^2-8x$ and $f(x)=x^2-4$, then what's the value of $g(x)$? I'm a little stuck with this simple function:
If ${f(g(x)) = 4x^2-8x}$ and ${f(x)=x^2-4}$, then what's the value of ${g(x)?}$
Any tips?
 [/INST] \begin{align}
f(g(x))&=4x^2-8x\\
g(x)^2-4&=4x^2-8x\\
g(x)^2&=4x^2-8x+4\\
&=4(x^2-2x+1)\\
&=4(x-1)^2\\
&=[\ \!2(x-1)\ \!]^2\\
\implies g(x)&=\pm2(x-1)
\end{align}
</s>