Question

Given these values
f(x)=x^2 -3x-4, g(x)=-2x, h(x)-x^3

Evaluate
(f(g(h(x)))

Answer 1

`\begin{cases} f(x)=x^2-3x-4\\ g(x)=-2x\\ h(x)=-x^3 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{g(~~h(x)~~)}{g(~~-x^3~~)}=-2\boxed{-x^3}\implies g(~~-x^3~~)=2x^3 \\\\[-0.35em] ~\dotfill\\\\ \underset{f(~~g(~~-x^3~~)~~)}{\stackrel{f(~~g(~~h(x)~~)~~)}{f(~~2x^3~~)}}=\boxed{2x^3}^2-3\boxed{2x^3}-4\implies f(~~2x^3~~)=2^2x^(3\cdot 2)-6x^3-4 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{f(~~g(~~h(x)~~)~~)}{f(~~2x^3~~)}=4x^6-6x^3-4~\hfill`