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 410: 11

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

Switching the elements of the domain and the range (in other words, the dependent and independent variables), we find that the inverse is: $$x=\frac{1}{y}-y \\ y=-\frac{x+\sqrt{x^2+4}}{2},\:y=-\frac{x-\sqrt{x^2+4}}{2}$$