Find all functions $f : R \to R$ such that $$f(x)f(y) = f(xy + 1) + f(x - y) - 2$$for all $x, y \in R$.
Problem
Source: New Zealand NZMOC Camp Selection Problems 2018 p10
Tags: functional equation, functional, algebra
Source: New Zealand NZMOC Camp Selection Problems 2018 p10
Tags: functional equation, functional, algebra
Find all functions $f : R \to R$ such that $$f(x)f(y) = f(xy + 1) + f(x - y) - 2$$for all $x, y \in R$.