1. The range of the function $f(x)=\sqrt{x-2}+\sqrt{3-x}$ is
$\qquad$
$-1 .[1, \sqrt{2}]$.
It is easy to know that the domain of $f(x)$ is $[2,3]$.
Let $x=2+\sin ^{2} \alpha\left(0 \leqslant \alpha \leqslant \frac{\pi}{2}\right)$.
Then $f(x)=\sin \alpha+\cos \alpha=\sqrt{2} \sin \left(\alpha+\frac{\pi}{4}\right)$.
Therefore, the range of $f(x)$ is $[1, \sqrt{2}]$.