Algebra · Functional inequalities · Substitution
Determine all functions \(f : \mathbb{R} \to \mathbb{R}\) such that for every real number \(x\),
\[ f(x+1) \le x \le f(x) + 1. \]
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Serbian Municipal Competition 2002, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source