Answer
$$y=\frac{3+5e^x}{e^x-1}$$
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:
$$x=\ln \left(y+3\right)-\ln \left(y-5\right) \\ y=\frac{3+5e^x}{e^x-1}$$