4. The even function $f(x)$ defined on $\mathbf{R}$ satisfies $f(x+1)=-f(x)$,
and is increasing in the interval $[-1,0]$, then ().
(A) $f(3)<f(\sqrt{3})<f(2)$
(B) $f(2)<f(3)<f(\sqrt{3})$
(C) $f(3)<f(2)<f(\sqrt{3})$
(D) $f(2)<f(\sqrt{3})<f(3)$
4. A.

From the problem, we know
$$
\begin{array}{l}
f(x)=-f(x+1)=f(x+2) . \\
\text { Then } f(3)=f(1)=f(-1), \\
f(2)=f(0), f(\sqrt{3})=f(\sqrt{3}-2) .
\end{array}
$$

And $-1<\sqrt{3}-2<0$, $f(x)$ is increasing in the interval $[-1,0]$
so, $f(3)<f(\sqrt{3})<f(2)$.