# How do you find the domain of sqrt(4 - x²)?

May 8, 2016

$x \in \left[- 2 , + 2\right]$

#### Explanation:

The domain is the set of values for which the expression is valid.

In the given example:
$\textcolor{w h i t e}{\text{XXX}} \sqrt{4 - {x}^{2}}$
we know that the argument of the square root must be greater than or equal to zero (assuming Real values; the square root of a negative value does not exist as a Real value).

Therefore
$\textcolor{w h i t e}{\text{XXX}} 4 - {x}^{2} \ge 0$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow {x}^{2} \le 4$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow - 2 \le x \le + 2$