# How do you find the domain of y=sqrt(5x+2)?

Sep 19, 2016

$x \ge - \frac{2}{5}$ or $\left[- \frac{2}{5} , \infty\right)$

#### Explanation:

$y = \sqrt{5 x + 2}$, find the domain

In order for y to be defined, the expression under the square root must not be negative. In other words, the expression under the square root must be greater than or equal to zero.

$5 x + 2 \ge \textcolor{w h i t e}{a} 0$
$\textcolor{w h i t e}{a a} - 2 \textcolor{w h i t e}{a a} - 2$

$5 x \ge - 2$

$\frac{5 x}{5} \ge - \frac{2}{5}$

$x \ge - \frac{2}{5}$ is the domain written as an inequality.

$\left[- \frac{2}{5} , \infty\right)$ is the domain written in interval notation