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2f(2x) = f(x) + x., continuous at 0

Source: Polish MO Recond Round 1986 p1

September 9, 2024
algebracontinuousfunctionalfunctional equation

Problem Statement

Determine all functions f:Rā†’R f : \mathbb{R} \to \mathbb{R} continuous at zero and such that for every real number x x the equality holds 2f(2x)=f(x)+x. 2f(2x) = f(x) + x.
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