Question 179
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ that satisfy
$$
f(x y-1)+f(x) f(y)=2 x y-1
$$
for all $x, y \in \mathbb{R}$.
$$
f(x y-1)+f(x) f(y)=2 x y-1
$$
for all $x, y \in \mathbb{R}$.
MathNet 2016-part-02 — 184 problems (EN–VI) Question 179
Math Olympiad Vault · MathNet 2016-part-02 — 184 problems (EN–VI)