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Question
Answer the following questions and show your work.
(a) Let f be a function f . Z → Z x Z such that f(n) = (2n, n + 3). Verify whether this function is 1-1 and whether it is onto.
(b) Let f be a function f . R3 → R such that f(x, y, z) = xyz. Verify whether this function is 1-1 and whether it is onto.
(c) Prove that the function f : R {f2} → R {5} de ned by f(x) = 5x+1/x-2 is a bijection.
(d) Consider the functions f : R → R, g : R → R x R de ned as f(x) = 1/x2+1 and g(x) = (3x, x2). Find the formulas for f o f and g o f.
Attachment:- ADM_A2.pdf
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