2. The function $f(x)$ is defined on $\mathbf{R}$, and satisfies:
(1) $f(x)$ is an even function;
(2) $f(x-1)$ is an odd function.

Then $f(2009)$ is ( ).
(A) 0
(B) 2008
(C) 2009
(D) -2008
2. A.

Since $f(x-1)$ is an odd function, we have $f(-1)=0$.
Also, since $f(x)$ is an even function, we get
$$
\begin{array}{l}
f(1)=0, f(-x)=f(x), \\
f(-x-1)=-f(x-1) .
\end{array}
$$

Then $f(x+4)=f(-x-4)=-f(x+2)$
$$
=-f(-x-2)=f(x) \text {. }
$$

Therefore, the period of $f(x)$ is $4$, and $f(2009)=f(1)=0$.