An algebra problem by Manuel Kahayon

Algebra Level 2

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

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