4. The range of the function $y=\sqrt{2004-x}+\sqrt{x-2003}$ is ( ).
(A) $[1,1.5]$
(B) $[1, \sqrt{2})$
(C) $[1, \sqrt{2}]$
(D) $[1,2)$
4.C.

It is known that the domain of the function is $[2003,2004], y>0$.
Also, $y^{2}=1+2 \sqrt{(2004-x)(x-2003)}$, and
$$
\begin{array}{l}
0 \leqslant(2004-x)(x-2003) \\
\leqslant\left(\frac{2004-x+x-2003}{2}\right)^{2}=\frac{1}{4},
\end{array}
$$

thus $1 \leqslant y^{2} \leqslant 2 \Rightarrow 1 \leqslant y \leqslant \sqrt{2}$.