Answer
$f^{-1} (x)=\sqrt {\dfrac{5-x}{2}}$
Domain of the function $f$ is: $[0, \infty)$.
Domain of the inverse of function $f$ is: $(-\infty, 5]$.
Work Step by Step
We have $y=-2x^2+5$
To compute the inverse, we will have to interchange $x$ and $y$.
$x=-2y^2+5$
Re-write as: $ y=\sqrt {\dfrac{5-x}{2}}$
Replace $y$ with $f^{-1} (x)$.
so, $f^{-1} (x)=\sqrt {\dfrac{5-x}{2}}$
