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f(x)=x has unique solution when f(f(x)) = 4x + 1

Source: 2013 Saudi Arabia Pre-TST 3.1

September 13, 2020
algebrafunctionalfunctional equation

Problem Statement

Let f:Rā†’Rf : R \to R be a function satisfying f(f(x))=4x+1f(f(x)) = 4x + 1 for all real number xx. Prove that the equation f(x)=xf(x) = x has a unique solution.
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