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Functional equation on positive reals

Source: Middle European Mathematical Olympiad 2012 - Individuals I-1

September 14, 2012

functionalgebrafunctional equationalgebra proposedInequality

Problem Statement

Let

\mathbb{R} ^{+}

denote the set of all positive real numbers. Find all functions

\mathbb{R} ^{+} \to \mathbb{R} ^{+}

such that

f(x+f(y)) = yf(xy+1)

holds for all

x, y \in \mathbb{R} ^{+}