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F 4. For each of the following correspondences, write exactly one of the following. • ONE-TO-ONE • ONTO • NEITHER ONE-TO-ONE NOR ONTO • BOTH ONE-TO-ONE AND ONTO • NOT A FUNCTION (a) £: R+R by f(x) = x². (b) h: Z-Z by h(n) = 3n. (c) q: {1,2}-{a,b} by g(1) = ag(2) = a. (d) k: {1,2}-{a,b} by k(1) = a,k(1) = b,k(2) = a (e) z: Z-Z by z(n) = n + 1. 5. Consider the correspondences f, h, g, and z from the previous problem. (a) If possible, find the value of £[2). (b) If possible, find the value of ² (√2). 2 (c) Determine the preimage set g-¹(b). (d) Determine the preimage set h-¹(81). (e) Compute the composite h(z(3)). (Hint: Work from the inside out.)