Answer
1) Domain: $(-\infty,2.25]$
2) Range: $[0,\infty )$
Work Step by Step
Given \begin{equation}
g(x)=\sqrt{-4 x+9}= \sqrt{4 \left(-x+\frac{9}{4}\right)}.
\end{equation} a) This is an even root function because the index, $n=2$, is even. The radicand must be positive. So, we require $$4 \left(-x+\frac{9}{4}\right)\geq 0\implies x\leq \frac{9}{4}=2.25.$$ 1) The domain is $(-\infty,2.25]$.
2) The range is $[0,\infty )$.
See the graph for proof.
