Originally Posted by

**pickslides** I think you are on the right track.

Given your original function is $\displaystyle f(x)=\pm\sqrt{2x-5}$ it will have $\displaystyle y \in\mathbb{R}$

But this is not a one to one function so its inverse does not exist.

Restricting the domain to force this function to be one to one you get.

Firstly

$\displaystyle f(x)=+\sqrt{2x-5},~y\in \mathbb{R}^- \cup \{0\}$

and then

$\displaystyle f(x)=-\sqrt{2x-5},~y\in \mathbb{R}^+ \cup \{0\}$

The best way to see this is via a sketch.