3. If for any $x \in \mathbf{R}$, the function $f(x)$ satisfies
$$
f(x+2.009)=-f(x+2008) \text {, }
$$

and $f(2009)=-2009$,
then $f(-1)=(\quad)$.
(A) 1 (B) -1
(C) 2009
(D) -2009
3. D.

Notice
$$
\begin{array}{l}
f(x+2009)=-f(x+2008) \\
=-f((x-1)+2009) \\
=f(x-1+2008)=f(x+2007) .
\end{array}
$$

Then $f(x)$ is a periodic function with a period of 2.
Thus $f(-1)=f(2009-2 \times 1005)$
$$
=f(2009)=-2009 .
$$