Answer
$$y=\frac{4-4x^2}{-x^2+7}$$
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:
$$x=\sqrt{\frac{4-7y}{4-y}} \\ y=\frac{4-4x^2}{-x^2+7}$$