Question: 2. Let A and B be sets. Suppose f : A B is a function. (a) f : A B is said to have a

2. Let A and B be sets. Suppose f : A B is a function. (a) f : A B is said to have a left inverse if there exists g : B A such that go f = I,. (i) (4 marks) Give an example of f that has a left inverse but does not have an inverse from B to A. (ii) (6 marks) Prove that if f is surjective and has a left inverse g, then f is bijective and q is its inverse. (b) (15 marks) Prove that f is injective if and only if for any set C' and any functions h : C + A and k:C7A, foh=fokh=k

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