MathDB
f(x-f(x))=f(x)-f(f(x))

Source: 2016 Thailand October Camp 2.3

February 26, 2022
functionfunctional equationalgebra

Problem Statement

Let ff be a function on a set XX. Prove that f(X−f(X))=f(X)−f(f(X)),f(X-f(X))=f(X)-f(f(X)), where for a set SS, the notation f(S)f(S) means {f(a)∣a∈S}\{f(a) | a \in S\}.
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