1. Suppose that g : A → C and h : B → C. Prove that if h is bijective, then there exists a function f : A → B such that g = h ° f . Hint: Draw a picture.
2. 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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