# What is the domain and range of  y =sqrt (x^2 - 9)?

Mar 18, 2018

$x \le - 3 \text{ or } x \ge 3$
$y \in \mathbb{R} , y \ge 0$

#### Explanation:

$\text{for the domain we require}$

${x}^{2} - 9 \ge 0$

$\Rightarrow {x}^{2} \ge 9$

$\Rightarrow x \le - 3 \text{ or } x \ge 3$

$\text{domain is } \left(- \infty , - 3\right] \cup \left[3 , + \infty\right)$

$\text{range is } y \in \mathbb{R} , y \ge 0$
graph{sqrt(x^2-9) [-10, 10, -5, 5]}