Question: Let A = {1, 2, 3, 4}. Let F be the set of all functions from A to A. Recall that IA F is the

Let A = {1, 2, 3, 4}. Let F be the set of all functions from A to A. Recall that IA F is the identity function on A given by IA(x) = x for all x A. Consider the function E : F A given by E(f) = f(1) for all f F.

(a) Is the function E one-to-one? Prove your answer.

(b) Is the function E onto? Prove your answer.

(d) How many onto functions f F are there so that E(f) = E(IA)? Explain.

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