For each of the following relations, please answer the following questions (briefly justify your answers). (i) (3 points) Is the relation a function? (ii) (3 points) If the relation is a function, what are its domain and image? (ii) (3 points) Is the inverse a function? If so, what is the inverse function? The relations of interest are
(a) {(z, y):,y Z,y-2) (c) f(x, y): z,y Z,r+ y 0) (e) {(x,y) E Z × Z : xly). (f) [(x, y): z, y e R, 2 y2 1) (2) (3 points each) Let A 1,2, 3,4]. Determine a codomain B and a function f: A- B such that the following hold (briefly justify your answers).
(a) f is onto B, but not one-to-one. (b) f is one-to-one, but not onto B (c) f is both one-to-one and onto B. (d) f is neither one-to-one nor onto B. Note: You might need to change your B from part to part.