Answer
$$y=\frac{\sqrt{x-9}}{2},\:y=-\frac{\sqrt{x-9}}{2}$$
Work Step by Step
Switching the elements of the domain and the range (in other words, the dependent and independent variables), we find that the inverse is:
$$x=4y^2+9\\ y=\frac{\sqrt{x-9}}{2},\:y=-\frac{\sqrt{x-9}}{2}$$
