MathNet 2023-part-03 — 191 problems (EN–VI) Question 150

Determine all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ that satisfy the property $f(x+a) \cdot f(x+b) = x$, $\forall x \in \mathbb{R}$, where $a, b \in \mathbb{R}$ are arbitrary fixed numbers.