$7 \cdot 73$ If the function $f(x)$ satisfies for all real numbers $x$: $f(2+x)=f(2-x)$ and $f(5+x)=f(5-x)$, then the period of the function $f(x)$ is
(A) 2.
(B) 5.
(C) 6.
(D) 7.
(China Sichuan Province High School Mathematics Competition, 1993)
［Solution］Suppose when $x=2$ and $x=5$, we have
$f(2+2)=f(2-2)$, which means $f(4)=f(0)$,
$f(5+5)=f(5-5)$, which means $f(10)=f(0)$.

Thus, $f(10)=f(4)$, i.e., $f(4+6)=f(4)$,
indicating that 6 is a period of the function $f(x)$. Also, $f(x)$ has no smaller period $(\because 6=2 \times 3$, clearly 2 and 3 are not periods of $f(x)$),
so the period of $f(x)$ is 6.
Therefore, the answer is $(C)$.