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