MathDB
Functional equation

Source: Czech and Slovak Olympiad 1987, National Round, Problem 3

April 10, 2020
functionalgebranational olympiad

Problem Statement

Let f:(0,∞)→(0,∞)f:(0,\infty)\to(0,\infty) be a function satisfying f(xf(y))+f(yf(x))=2xyf\bigl(xf(y)\bigr)+f\bigl(yf(x)\bigr)=2xy for all x,y>0x,y>0. Show that f(x)=xf(x) = x for all positive xx.
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