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Function Equation German TST 2003 - f(f(x)+y)=2x+f(f(y)-x)

Source: German TST 2003

January 14, 2011
functionalgebra unsolvedalgebra

Problem Statement

Determine all functions f:Rā†’Rf: \mathbb R \to \mathbb R with the property f(f(x)+y)=2x+f(f(y)-x),   \forall x,y \in \mathbb R.
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