#### Answer

$f(x) $, domain $[0, \infty)$, range $[-1,\infty)$
$f^{-1} $, domain $[-1,\infty)$, range $[0,,\infty)$

#### Work Step by Step

Step 1. Find the inverse of the first function as $g(x)=f^{-1}=\sqrt {x+1}$
Step 2. For function $f(x)=x^2-1, x\geq0$, shown as the red curve in the figure, we can identify its domain as $[0, \infty)$ and its range as $[-1,\infty)$
Step 3. For function $g(x)=f^{-1}=\sqrt {x+1}$, shown as the blue curve in the figure, we can identify its domain as $[-1,\infty)$ and its range as $[0,\infty)$