Is there a function such that $f(x+y) = f(xy)$?

Question

If we define $x, y \in \mathbb{R}$, is there a function that fulfills the condition:

$f(x+y) = f(xy)$

for all $x$ and $y$?

For now, let's assume there are no stipulations on continuity and differentiability.

Answer 1

If $y=0$ then $f(x)=f(x+0)=f(0x)=f(0)$, so $f$ is a constant.