MathDB
Functional Equation

Source: China TST 2004 Quiz

February 1, 2009
functionquadraticsalgebra unsolvedalgebra

Problem Statement

Given non-zero reals a a, b b, find all functions f:R⟼R f: \mathbb{R} \longmapsto \mathbb{R}, such that for every x,y∈R x, y \in \mathbb{R}, y≠0 y \neq 0, f(2x) \equal{} af(x) \plus{} bx and \displaystyle f(x)f(y) \equal{} f(xy) \plus{} f \left( \frac {x}{y} \right).
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