Answer
1) Domain: $(-\infty,-10]$
2) Range: $[0,\infty )$
Work Step by Step
Given \begin{equation}
g(x)=\sqrt{-x-10}= \sqrt{-(x+10)}.
\end{equation} a) This is an even root function because the index, $n=2$, is even. The radicand must be positive. So, we require $$-(x+10)\geq 0\implies x+10\leq 0 \implies x\leq -10.$$ 1) The domain is $(-\infty,-10]$.
2) The range is $[0,\infty )$.
See the graph for proof.
