## Algebra and Trigonometry 10th Edition

$\sqrt {\dfrac{x}{2}} +4$ Domain of the function $f$ is: $x \geq 4$. Domain of the inverse of function $f$ is: $x \geq 0$.
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, $f^{-1} (x)=\sqrt {\dfrac{x}{2}} +4$