# How do you find the domain of  f(x)=(x^2-9)/sqrt(x^2-4)?

Jan 20, 2018

$\left(- \infty , - 2\right) \cup \left(2 , + \infty\right)$

#### Explanation:

${x}^{2} - 9 \text{ is defined for all real values of x}$

$\text{the denominator cannot equal zero as this would make}$
$\text{f(x) undefined}$

$\Rightarrow {x}^{2} - 4 \ne 0$

$\Rightarrow \left(x - 2\right) \left(x + 2\right) \ne 0$

$\Rightarrow x \ne \pm 2$

$\text{also } {x}^{2} - 4 > 0$

$\Rightarrow x < - 2 , x > 2$

$\text{domain is } \left(- \infty , - 2\right) \cup \left(2 , + \infty\right)$

graph{(x^2-9)/(sqrt(x^2-4)) [-10, 10, -5, 5]}