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
3. A $f(10+x)=f(10-x), x=10$ is the axis of symmetry for $f(x)$, and from $f(5-x)=f(5+x)$, we know that $x=5$ is also an axis of symmetry for $f(x)$. According to the explanation in Example 7, it is a periodic function, with $T=10$ being one of its periods. Also, $f(x)=f(10+x)=f(10-x)=f(-x)$, so $f(x)$ is also an even function.