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f(x)f(y) = f(xy + 1) + f(x - y) - 2

Source: New Zealand NZMOC Camp Selection Problems 2018 p10

September 19, 2021
functional equationfunctionalalgebra

Problem Statement

Find all functions f:R→Rf : R \to R such that f(x)f(y)=f(xy+1)+f(x−y)−2f(x)f(y) = f(xy + 1) + f(x - y) - 2 for all x,y∈Rx, y \in R.
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