Idempotence of a Function

How many of the following functions are idempotent?

  • \(\lfloor x \rfloor\)

  • \(|x|\)

  • \(x^2\)

  • \(\lceil x \rceil\)

  • \(\sqrt{x}\)

  • \(f(f(x))=f(x)\)

Definition: Idempotence

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