156 Let the function $f(x)$ be defined on the real number set $R$ as an odd function, and another function $g(x)=f(x+2)$ is an even function. Moreover, when $x \in[0,2]$, $f(x)=x$. Then the number of such functions $f(x)$ is ( )
A. 0 (i.e., none)
B. 1
C. More than one, but only a finite number
D. Infinitely many
156 B. From $g(x)=f(x+2)$ being an even function, we get $f(-x+2)=f(x+2)$, which means that $y=f(x)$ is symmetric about the line $x=2$. Therefore,
$$
f(x)=\left\{\begin{array}{ll}
x-8 k, & x \in[-2+8 k, 2+8 k] \\
-(x-8 k)+4, & x \in[2+8 k, 6+8 k]
\end{array} k \in \mathbf{Z}\right.
$$