# How do you find the domain of  sqrt{-x - 2}?

Jun 19, 2016

All values of x smaller than or equal to -2 (or $x \le - 2$)

#### Explanation:

Domain of $\sqrt{f \left(x\right)}$ is always all values of x for which $f \left(x\right) \ge 0$ as if $f \left(x\right)$ is negative, $\sqrt{f \left(x\right)}$ is no longer real.

Thus, here $f \left(x\right) = - x - 2$

$f \left(x\right) \ge 0$ which means that $- x - 2 \ge 0$

Adding 2 on both sides, we get
$- x \ge 2$

If we multiply -1 on both sides, we'll have to reverse the sign of inequality, so this becomes

$x \le - 2$

Hence for all values of x smaller than or equal to -2, $\sqrt{- x - 2}$ will be real and hence, these values are the domain for this function.