Answer
$f^{-1} (x)=\sqrt x+4$
Domain of the function $f$ is: $[4, \infty)$.
Domain of the inverse of function $f$ is: $[0, \infty)$.
Work Step by Step
We have $y=(x-4)^2$
To compute the inverse, we will have to interchange $x$ and $y$.
$x=(y-4)^2$
Re-write as: $ y=\sqrt x+4$
Replace $y$ with $f^{-1} (x)$.
so, $f^{-1} (x)=\sqrt x+4$
