3 Let $f(x)$ be defined on $[0,1]$. For the function $f(x-a)+f(x+a)$ to be defined, the range of values for $a$ is ( ).
(A) $\left(-\infty,-\frac{1}{2}\right)$
(B) $\left[-\frac{1}{2}, \frac{1}{2}\right]$
(C) $\left(\frac{1}{2},+\infty\right)$
(D) $\left(-\infty,-\frac{1}{2}\right] \cup\left[\frac{1}{2},+\infty\right)$
(3) The domain of the function $f(x-a)+f(x+a)$ is $[a, 1+a] \cap[-a, 1-a]$. When $a \geqslant 0$, it should be that $a \leqslant 1-a$, i.e., $a \leqslant \frac{1}{2}$; when $a \leqslant 0$, it should be that $-a \leqslant 1+a$, i.e., $a \geqslant-\frac{1}{2}$. Therefore, the answer is B.