4. Let the domain of $f(x)$ be $\mathbf{R}$, and for any $x \in \mathbf{R}$, $f(x-2)=f(x)$. It is known that on $[-1,1]$, the expression for $f(x)$ is $f(x)=x^{2}-2 x+4$. Then the expression for $f(x)$ on $[-3,-1]$ is ( ).
A. $x^{2}-2 x+4$
B. $x^{2}-6 x+12$
C. $x^{2}+2 x+4$
D. $x^{2}+6 x+12$
4. C. $\because x \in[-3,-1]$, we have $x+2 \in[-1,1], \therefore \quad f(x)=f(x+2)=(x+2)^{2}-2(x+2)+4=$ $x^{2}+2 x+4$, so the answer is C.