MathDB
Rational Functional Equation

Source: Iran National Olympiad (3rd Round) 2001

July 13, 2007
functioninductionnumber theory proposednumber theoryfunctional equation

Problem Statement

Find all functions f:Q⟶Q f: \mathbb Q\longrightarrow\mathbb Q such that: f(x)+f(1x)=1 f(x)+f(\frac1x)=1 2f(f(x))=f(2x) 2f(f(x))=f(2x)
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