# How to find domain and range of say: y = 1/(x^2 - 2)?

Apr 19, 2018

Below

#### Explanation:

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

$y = \frac{1}{\left(x - \sqrt{2}\right) \left(x + \sqrt{2}\right)}$

Domain: all reals except when $x = - \sqrt{2}$ and $x = \sqrt{2}$

Range: all reals except $- \frac{1}{2} < y < 0$

graph{1/(x^2-2) [-10, 10, -5, 5]}