(a) Prove that the function h in Example 17.10 is one-to- one and onto and preserves the operation of addition.
(b) Let (F, +, •) and (K, ⊕, ⊙) be two fields. If g: F → K is a ring isomorphism and a is a nonzero element of F (that is, a is a unit in F), prove that g(a-1) = [g(a)]-1. (Consequently, this function g establishes an isomorphism of fields. In particular, the function h of Example 17.10 is such a function.)