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

Source: Czech and Slovak Olympiad 2017, National Round, III A p3

February 2, 2020
functional equationfunctionalalgebra

Problem Statement

Find all functions f:R→Rf: R \to R such that for all real numbers x,yx, y holds f(y−xy)=f(x)y+(x−1)2f(y)f(y - xy) = f(x)y + (x - 1)^2 f(y)
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