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f (xf (y) - yf (x)) = f (xy) - xy

Source: 2020 Grand Duchy of Lithuania, Mathematical Contest p1 (Baltic Way TST)

October 3, 2020
algebrafunctionalfunctional equation

Problem Statement

Find all functions f:R→Rf: R \to R, such that equality f(xf(y)−yf(x))=f(xy)−xyf (xf (y) - yf (x)) = f (xy) - xy holds for all x,y∈Rx, y \in R.
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