Answer
$y=\pm \sqrt{ 5 - \frac{1}{2}x}$.
The inverse is not a function
Work Step by Step
Firstly swap the given variables :
$x=10-2 y^{2}$
Solve for $y$.
Now isolate $2y^{2}$ on one side :
$2y^{2}=10-x$
Divide both sides by 2 :
$y^{2}=5 -\frac{1}{2}x$
Now, take the square root of the both sides :
$y=\pm \sqrt{ 5 - \frac{1}{2}x}$
The inverse is not a function because, for most values of $x$, there corresponds two values of $y$.