Answer
1) Domain: $(-\infty,-11]$
2) Range: $[0,\infty )$
Work Step by Step
Given \begin{equation}
h(x)=\sqrt{-x-11}= \sqrt{-(x+11)}.
\end{equation} a) This is an even root function because the index, $n=2$ is even. The radicand must be positive. So, we require $$-(x+11)\geq 0\implies x+11\leq 0 \implies x\leq -11.$$ 1) The domain is $(-\infty,-11]$
2) The range is $[0,\infty )$.
See the graph for proof.
