4. The function $f(x)$ is a real function defined on $R$, it is symmetric about the line $x=1$ and also symmetric about the line $x=3$, then the function $f(x)($ ).
(A) is not a periodic function
(B) is a periodic function with period 1
(C) is a periodic function with period 2
(D) is a periodic function with period 4
4. D.

Given $f(x)=f(2-x), f(t)=f(5-t)$, let $t=2-x$, then $f(x)=f(2-x)=f[6-(2-x)]=f(x+4)$, hence
$f(x+4)=f(x)$ for all $x$.