Let A be the set of even integers and B be the set of odd integers. A function f : A x B → B x A is defined by f((a, b)) = f(a, b) = (a+b, a), and a function g : B x A → B x B is defined by g(c, d) = (c+d, c).

(i) Determine whether the function g ◦ f : A x B → B x B is one-to-one.

(ii) Determine whether g ◦ f is onto.