Indicate which of the functions in the referenced exercise

Chapter 7, Problem 44E

(choose chapter or problem)

Problem 44E

Indicate which of the functions in the referenced exercise are one-to-one correspondences. For each function that is a one-to-one correspondence, find the inverse function.

Exercise

a. Define f: Z → Z by the rule f(n) = 2n, for all integers n.

(i) Is f one-to-one? Prove or give a counterexample.

(ii) Is f onto? Prove or give a counterexample.

b. Let 2Z denote the set of all even integers. That is, 2Z = {n ∈ Z | n = 2k, for some integer k}. Define h: Z → 2Z by the rule h(n) = 2n, for all integers n. Is h onto? Prove or give a counterexample.