$7 \cdot 108$ For any real numbers $x, y$, the function $f(x)$ satisfies the relation
$$
f(x+y)=f\left(x^{2}\right)+f(2 y) .
$$

Then the value of $f(1985)$ is
(A) 1985 .
(B) $\sqrt{1985}$.
(C) 3990 .
(D) None of the above.
(China Beijing High School Mathematics Competition, 1985)
[Solution] Let $y=x$, we get $f(2 x)=f\left(x^{2}\right)+f(2 x)$,
i.e., $\square$
$$
f\left(x^{2}\right)=0 \text {. }
$$

Let $x=\sqrt{1985}$, substituting in we get $f(1985)=0$.
Clearly, (A), (B), and (C) are not true.
Therefore, the answer is (D).