# How do you find the domain of  sqrt(x + 5) ?

Mar 13, 2018

$x \in \mathbb{R} , x \ge - 5$

#### Explanation:

$\text{the expression inside the radical must be greater than}$
$\text{or equal to zero}$

$\text{solve "x+5>=0" for domain}$

$\text{subtract 5 from both sides}$

$x \cancel{+ 5} \cancel{- 5} \ge 0 - 5$

$\Rightarrow x \ge - 5$

$\text{domain is } x \in \mathbb{R} , x \ge - 5$

$\left[- 5 , + \infty\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$
graph{sqrt(x+5) [-10, 10, -5, 5]}