Answer
$f^{-1} (x)=\sqrt {2x+2}$
Domain of the function $f$ is: $[0, \infty)$.
Domain of the inverse of function $f$ is: $[-1,\infty)$.
Work Step by Step
We have $y=\dfrac{1}{2}x^2-1$
To compute the inverse, we will have to interchange $x$ and $y$.
$y=\dfrac{1}{2}y^2-1$
Re-write as: $ y=\sqrt {2x+2}$
Replace $y$ with $f^{-1} (x)$.
so, $f^{-1} (x)=\sqrt {2x+2}$
