Functions. Basics

Algebra Level 4

Let \(f : A \to B \) and \(g : B \to A \) be functions such that \(g \circ f = Id_{A}\). How many of the following statements are always true?

  • \(f\) is injective.
  • \(g\) is injective.
  • \(f\) is surjective.
  • \(g\) is surjective.
  • \(f\) is bijective.
  • \(g\) is bijective
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