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

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Answer 1 · 2016-06-19T05:26:32

All values of x smaller than or equal to -2 (or $x<=-2$ )

Domain of $sqrt(f(x))$ is always all values of x for which $f(x)>=0$ as if $f(x)$ is negative, $sqrt(f(x))$ is no longer real.

Thus, here $f(x)=-x-2$

$f(x)>=0$ which means that $-x-2>=0$

Adding 2 on both sides, we get
$-x>=2$

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

$x<=-2$

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.

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