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Define a function f: 232% Z by Ax) = (2x+3,x-5). (a) Is f one-to-one? Prove or disprove. The function {Select- v] one-to-one. Let 3, bE Z, and suppose that f(a) = f(b). Then (@2+3,2-5)=( ). In order for the two ordered pairs to be equal, an item in one ordered pair must be equal to the corresponding item in the other ordered pair, which is to say 2a+3= and In both cases, after simplifying it is clear that a = . Therefore f|Select-- v] one-to-one. (b) Does f map Z onto Z x Z? Prove or disprove. The function f[-Select- v] onto, because there is no x Z such that f(x) = (2x + 3, x 5) = (0, 0). Suppose to the contrary that there is such anx.So,2x+3=[ =|. Solve for x andfindthatxmustbe[ ___| . This cannot be because _ Therefore F[Selec= ] onto