# How do you find the domain of sqrt(x+4)?

Mar 26, 2018

The domain is $x \ge 4$

#### Explanation:

Since square roots are only defined when the expression under the square root is non-negative, to find the domain we set the expression under the square root greater than or equal to zero:

$x - 4 \ge 0$
$x \ge 4$

Mar 26, 2018

$\left[- 4 , \infty\right)$

#### Explanation:

Firstly you know that there can't be a negative under a square root $\sqrt{- 1}$ any negative leads to the function being undefined

So when $x + 4 < 0$ i.e. it is lower than zero you know there is no domain

So when $x + 4 \ge 0$ the domain exists so it eixsts when $x \ge - 4$

So the domain is $\left[- 4 , \infty\right)$