# What is the domain of sqrt(4-x^2)?

Apr 19, 2018

color(blue)([-2,2]

#### Explanation:

If:

$\sqrt{4 - {x}^{2}}$ is defined only for real numbers then:

$4 - {x}^{2} \ge 0$

${x}^{2} \le 4$

$x \le 2$

$x \ge - 2$

$\therefore$

$\left[- 2 , 2\right]$

Apr 19, 2018

$- 2 \le x \le 2$

#### Explanation:

The square roots are only defined when the expression under the square root is non-negative.

$4 - {x}^{2} \ge 0$
$| x | \le 2$
$- 2 \le x \le 2$