Consider the following functions: fa(n) = 1g(n) + Ig(na) fo(n) = 3"+1 +5n4 fe(n) = 3n0.2 + 3n0.8 fa(n) = 216 fe(n) = 4 lg(n + 2n) + 6n0.7 fs(n) = n + 21-2 f,(n) = 3n lg(n + 2) + na fr(n) = ((9n)(6n)(121))1/2 fi(n) = (4 + 5n + Ig(n))/2 f;(n) = lg?(n) + n lg(n") + 500n fi(n) = ((5n")(6n)(121n1'))1/5 +n Ig(n100) fi(n) = n"-1 fm(n) = 23vn 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 f, find the simplest" function g such that f(n) = (g(n)). (b) Order the functions by asymptotic dominance: give a sequence fi, f2.... such that fi(n) = (fi+1(n)). Make a note if any two functions are asymptotically equivalent, i.e. if f(n) = (fi+1(n))