Example 9 The range of the function $y=\sqrt{1994-x}+\sqrt{x-1993}$ is __. (Example 11 in [1])
By Cauchy-Schwarz inequality, we have $(\sqrt{1994-x}+$
$$\begin{array}{l}
\sqrt{x-1993})^{2} \leqslant\left(1^{2}+1^{2}\right)[(1994-x)+(x-1993)] \\
=2, \therefore y \leqslant \sqrt{2} .
\end{array}$$

On the other hand, $y^{2}=1+2 \sqrt{1994-x} \cdot \sqrt{x-1993} \geqslant$ $1, \therefore y \geqslant 1$, hence the range of values is $[1, \sqrt{2}]$.