Question 61
Find all functions $f: \mathbb{R} \to \mathbb{R}$ such that
$$
f(x)f(y) = f(xy - 1) + x f(y) + y f(x), \quad \forall x, y \in \mathbb{R}.
$$
$$
f(x)f(y) = f(xy - 1) + x f(y) + y f(x), \quad \forall x, y \in \mathbb{R}.
$$
MathNet 2021 — Part 09 Question 61
Math Olympiad Vault · MathNet 2021 — Part 09