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f (f (x) + y) = f (x) + f (y), bounded

Source: 2020 Swedish Mathematical Competition p3

May 1, 2021
boundedalgebrafunctional equationfunctionalISL

Problem Statement

Determine all bounded functions f:Rā†’Rf: R \to R, such that f(f(x)+y)=f(x)+f(y)f (f (x) + y) = f (x) + f (y), for all real x,yx, y.
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