Answer
The domain is the set of real numbers less than or equal to $-2$.
Work Step by Step
The given function is
$n(x)=\frac{1}{2}\sqrt{-x-2}$
The radicand cannot be negative.
So, $-x-2$ is greater than or equal to zero.
$\Rightarrow -x-2\geq 0$
Add $x$ to each side.
$\Rightarrow -x-2+x\geq 0+x$
Simplify.
$\Rightarrow -2\geq x$
Hence, the domain is the set of real numbers less than or equal to $-2$.
