3 If for any $x \in \mathbf{R}$, the function $f(x)$ satisfies
$$
f(x+2009)=-f(x+2008),
$$

and $f(2009)=-2009$, then $f(-1)=(\quad$.
(A) 1
(B) -1
(C) 2009
(D) -2009
(3) D Hint: $f(x+2009)=-f(x+2008)$
$$
\begin{array}{l}
=-f((x-1)+2009) \\
=f(x-1+2008) \\
=f(x+2007),
\end{array}
$$

Therefore, $f(x)$ is a periodic function with a period of 2, so we have
$$
f(-1)=f(2009-2 \times 1005)=f(2009)=-2009 .
$$

Hence, the answer is D.