Verify whether this function is 1-1 and whether it is onto

Question

Question 1 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 - {2} → R - {5} defined by f(x) = 5x + 1/x-2 is a bijection.

(d) Consider the functions f :R → R,g :R → R x R defined as f (x) = 1/x²+1 and g(x) = (3x,x²). Find the formulas for f o f and g o f.