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