Example + Given that $f(x)$ is an even function defined on $\mathbf{R}$, if $g(x)$ is an odd function, and $g(x)=f(x-1)$, $g(1)=2003$, find the value of $f(2004)$.
$g(x)$ is an odd function, so, $g(-x)=-g(x)$, and $g(x)=f(x-1)$, therefore, $g(-x)=$ $-f(-x-1)$. Since $f(x)$ is an even function, then $f(x-1)=-f(x+1)$
Thus,
$$
f(x-1)=-f(x+1)=-[-f(x+1+2)]=f(x+3)
$$
$f(x)$ is a periodic function with a period of 4,
$$
f(0)=g(1)=2003, f(2004)=f(0)=2003
$$