Calculus and Its Applications, Chapter 1, Test, Section Test, Problem 40

If $f(x) = x^2 - x$ and $g(x) = 2x^3$. Find $f(f \circ g)(x)$ and $(g \circ f)(x)$

$
\begin{equation}
\begin{aligned}
(f \circ g)(x) = f(g(x)) &= f(2x^3) \\
\\
&= (2x^3)^2 - (2x^3) \\
\\
&= 4x^6 - 2x^3\\
\\
(g \circ f)(x) = g(f(x)) &= g(x^2 - x) \\
\\
&= 2(x^2 - x)^3
\end{aligned}
\end{equation}
$