Let f be a function f z rarr z x z such that fn 2n n 3

Question

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