Chapter 10 - Compositions, Inverses, and Combinations of Functions - 10.2 Invertibility and Properties of Inverse Functions - Exercises and Problems for Section 10.2 - Exercises and Problems - Page 411: 40

$$y=e^{\frac{-5-7x}{2x-1}}$$

Switching the elements of the domain and the range (in other words, the dependent and independent variables), we find that the inverse is: $$x=\frac{\ln \left(y\right)-5}{2\ln \left(y\right)+7} \\ y=e^{\frac{-5-7x}{2x-1}}$$