For these functions, do the following: (a) Prove the asymptotic complexity of each of the functions, in sim- plest terms. That is, for each function S, find the "simplest function g such that f(n) = (g(n)). (b) Order the functions by asymptotic dominance: give a sequence f1, f2, ... such that fi(n) = (fi+1(n)). Make a note if any two functions are asymptotically equivalent, i.e. if fi(n) = (fi+1(n)). fa(n) =lg(n) + lg(n) fo(n) = 3n+1 + 5n4 fe(n) = 3n0.2 + 3n0.8 fa(n) = 216 Sen) = 4 lg(n2 + 2n) + 6n0.7 fr(n) = n) + 2n2 Sa(n) = 3n lg(n+ 2) + n2