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Integer to integer functions

Source: 11th Brazilian Math Olympiad - Problem 3

December 27, 2017
Brazilian Math OlympiadBrazilian Math Olympiad 1989functionsalgebra

Problem Statement

A function ff, defined for the set of integers, is such that f(x)=x−10f(x)=x-10 if x>100x>100 and f(x)=f(f(x+11))f(x)=f(f(x+11)) if x≤100x \leq 100.
Determine, justifying your answer, the set of all possible values for ff.
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