Answer
1) Domain: $[-3, \infty)$
2) Range $[0,\infty )$
Work Step by Step
Given \begin{equation}
g(x)=\sqrt{x+3}.
\end{equation} a) This is an even root function because the index, $n=2$, is even. The radicand must be positive. So, we require $$x+3\geq 0\implies x\geq -3.$$ 1) The domain is $[-3, \infty)$.
2) The range is $[0,\infty )$.
