Question 125
Let $a \neq 0$ be a real number. Determine all functions $f : \mathbb{R} \to \mathbb{R}$ satisfying
$$
f(x)f(y) + f(x+y) = axy
$$
for all real numbers $x$ and $y$.
$$
f(x)f(y) + f(x+y) = axy
$$
for all real numbers $x$ and $y$.
MathNet 2016-part-06 — 184 problems (EN–VI) Question 125
Math Olympiad Vault · MathNet 2016-part-06 — 184 problems (EN–VI)