Answer
$f(x)$ and $g(x)$ are inverse functions.
Work Step by Step
Let us find the inverse of $f(x)$ by solving for $x$.
\[ y = x^3 \\ \\ \sqrt[3] y = x \]
Therefore, the inverse of $f(x)$ is $\sqrt[3]x$, which is $g(x)$. Therefore, $f(x)$ is the inverse of $g(x)$ and vice versa.
Graphically, we see that every point on $f(x)$, when reflected over the line $g(x)$ lies on one point on $g(x)$. Specifically, if a point $(a,b)$ is on $f(x)$, then there is a point $(b, a)$ on $g(x)$.
