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Vietnam TST 1994 functional equation

Source: Vietnam TST 1994 for the 35th IMO, problem 5

June 25, 2005
functionlogarithmsalgebra unsolvedalgebra

Problem Statement

Determine all functions f:R↦Rf: \mathbb{R} \mapsto \mathbb{R} satisfying f(2⋅x)+f(4+3⋅2⋅x)=2⋅f((2+2)⋅x)f\left(\sqrt{2} \cdot x\right) + f\left(4 + 3 \cdot \sqrt{2} \cdot x \right) = 2 \cdot f\left(\left(2 + \sqrt{2}\right) \cdot x\right) for all xx.
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