1. The range of the function $f(x)=\sqrt{x-5}-\sqrt{24-3 x}$ is $\qquad$ .
$-1 \cdot[-3, \sqrt{3}]$. 
It is known that the domain of $f(x)$ is $[5,8]$, and $f(x)$ is an increasing function on $[5,8]$.
Therefore, the range of $f(x)$ is $[-3, \sqrt{3}]$.