For each integer n, define f_n: r rightarrow r by f_n (x) = x + n. (a) prove that for each integer n, f_n is a permutation of r, that is f_n elementof s(r). (b) prove that f_n compositefunction f_m = f_n + m and f^-1_n = f_-n (c) let g = {f_n: n elementof z}. prove that g is a subgroup of s(r). (d) prove that g is cyclic (find a generator of g).