MathDB
f(2x - f (x)) = x, f(x) > x, f(x) > f(y) for all real x > y

Source: 2015 Latvia BW TST P2

December 16, 2022
functional equationfunctionalalgebra

Problem Statement

It is known about the function f:R→Rf : R \to R that ∙\bullet f(x)>f(y)f(x) > f(y) for all real x>yx > y ∙\bullet f(x)>xf(x) > x for all real xx ∙\bullet f(2x−f(x))=xf(2x - f (x)) = x for all real xx. Prove that f(x)=x+f(0)f(x) = x + f(0) for all real numbers xx.
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