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5. Let n E N. Suppose that n is a perfect square that is n = m' for some m E Z. Show that 2n is not a perfect square. 6. Let f : Z - Z defined so that f(n) = -n + 3 if n is even and f(n) = n +7 if n is odd. Prove that f is bijective and express its compositional inverse f-1. 7. Let A = R - {0, 1} and let f : A - A be defined by f(x) = 1 - 1. (a) Show that fo f of = i4 where iA is the identity function on the set A. (b) Prove that any function g : A - A satisfying gogog = iA is bijective. (c) Use part (b) to conclude that f is bijective and determine f-1. 8. Prove that if k is a positive integer and vk is not an integer, then vk is irrational