TH-TMO 2014 Problem 2

Find all functions $f : R \to R$ satisfying $f(xy - 1) + f(x)f(y) = 2xy - 1$ for all real numbers $x, y$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.