3. A non-constant function defined on $\mathbf{R}$ satisfies: (1) $f(10+x)$ is an even function (2) $f(5-x)=f(5+x)$, then $f(x)$ must be
A. an even function and a periodic function
B. an even function but not a periodic function
C. an odd function and a periodic function
D. an odd function but not a periodic function