Answer
$$y=\frac{x^2}{x^2-2x+1}$$
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:
$$x=\frac{\sqrt{y}}{\sqrt{y}+1} \\ y=\frac{x^2}{x^2-2x+1}$$