7・72 If $f(x)$ is a non-constant function defined on all real numbers, then
$$
F(x)=f(x)-f(-x)
$$
(A) is an odd function.
(B) is an even function.
(C) is both an odd and an even function.
(D) is neither an odd nor an even function.
(China Beijing High School Mathematics Competition, 1990)
[Solution] From $F(-x)=f(-x)-f(-(-x))=f(-x)-f(x)$
$$
=-[f(x)-f(-x)]=-F(x),
$$
$\therefore \quad F(x)$ is an odd function.
Therefore, the answer is $(A)$.