2. Define the function f : Z_{17}^{×} -> Z_{17}^{×} by f(x) = x^{-1}, for all x in Z_{17}^{×}. Is f one to one? Is f onto? If possible, find the inverse function f^{-1}.
3. (a) Let be a fixed element of S_{n}. Show that f : S_{n} -> S_{n} defined by f() = ^{-1}, for all in S_{n}, is a one-to-one and onto function.
(b) In S_{3}, let = (1,2). Compute the corresponding function f defined in part (a).