(2) The range of the function $f(x)=\sqrt{x-3}+\sqrt{12-3 x}$ is ( ).
(A) $[1, \sqrt{2}]$
(B) $\left[1, \frac{3}{2}\right]$
(C) $[1, \sqrt{3}]$
(D) $[1,2]$
(2) D Hint: $3 \leqslant x \leqslant 4$, then $0 \leqslant x-3 \leqslant 1$. Let $x-3=\sin ^{2} \theta$
$$
\begin{array}{l}
\left(0 \leqslant \theta \leqslant \frac{\pi}{2}\right) \text {, } \\
f(x)=\sqrt{x-3}+\sqrt{3(4-x)} \\
=\sin \theta+\sqrt{3\left(1-\sin ^{2} \theta\right)} \\
=\sin \theta+\sqrt{3} \cos \theta \\
=2 \sin \left(\theta+\frac{\pi}{3}\right), \\
1=2 \sin \left(\frac{\pi}{2}+\frac{\pi}{3}\right) \leqslant f(x) \leqslant 2 \sin \left(\frac{\pi}{6}+\frac{\pi}{3}\right)=2 . \\
\end{array}
$$

Therefore, the range of $f(x)$ is $[1,2]$.