Answer
$f(x) $, domain $(-\infty, \infty)$, range $(-\infty,\infty)$
$f^{-1} $, domain $(-\infty, \infty)$, range $(-\infty,\infty)$
Work Step by Step
Step 1. Find the inverse of the first function as $g(x)=f^{-1}=(x+1)^{1/3}$
Step 2. For function $f(x)=x^3-1$, shown as the red curve in the figure, we can identify its domain as $(-\infty, \infty)$ and its range as $(-\infty,\infty)$
Step 3. For function $g(x)=f^{-1}=(x+1)^{1/3}$, shown as the blue curve in the figure, we can identify its domain as $(-\infty, \infty)$ and its range as $(-\infty,\infty)$
