Suppose that f: A → B is any function. Then a function g: B → A is called a left inverse for f if g(f(x)) = x for all x ∈ A, right inverse for f if f (g(y)) = y for all y ∈ B.
(a) Prove that f has a left inverse iff f is injective.
(b) Prove that f has a right inverse iff f is surjective.
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