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x + f(y) =a(y + f(x)) , parameter functional

Source: 2009 Belarus TST 5.3

November 8, 2020
functionalalgebrafunctional equation

Problem Statement

Find all real numbers aa for which there exists a function f:R→Rf: R \to R asuch that x+f(y)=a(y+f(x))x + f(y) =a(y + f(x)) for all real numbers x,y∈Rx,y\in R.
I.Voronovich
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