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Function using maximum

Source: 2022 IRN TWN Friendly math competition P2

June 23, 2022
algebrafunctional equationfunctionTaiwanIran

Problem Statement

Find all functions f:R→Rf:\mathbb{R} \rightarrow \mathbb{R} such that: ∙\bullet f(x)<2f(x)<2 for all x∈(0,1)x\in (0,1); ∙\bullet for all real numbers x,yx,y we have: max{f(x+y),f(x−y)}=f(x)+f(y)max\{f(x+y),f(x-y)\}=f(x)+f(y)
Proposed by Navid Safaei
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