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A function f : A → B is called constant if there exists b ∈ B...

A function f : A → B is called constant if there exists b ∈ B such that for all x ∈ A, f(x) = b. Let f : A → B, and suppose that A is nonempty.

Prove that f is constant if and only if for all g : A → A, f ◦ g = f.

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