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Nepal National Olympiad

Source: Nepal Mathematics Olympiad

April 22, 2018
functionsalgebra

Problem Statement

Problem Section #2
c). Denote by Q+\mathbb{Q^+} the set of all positive rational numbers. Determine all functions f:Q+→Q+f:\mathbb{Q^+}\to\mathbb{Q^+} which satisfy the following equation for all x,y∈Q+:f(f(x)2.y)=x3.f(xy)x,y \in \mathbb{Q^+} : f(f(x)^2.y)=x^3.f(xy).
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