An algebra problem by Manuel Kahayon

Algebra Level 2

Does there exist a function \(f: \mathbb{R} \to \mathbb{R}\) which satisfies

  1. \(f(x)\) is bijective;
  2. \(f(x)\) is neither non-increasing nor non-decreasing;
  3. \(f\big(f(x)\big)\) is non-decreasing?
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