1. (30 pts) Consider the following functions . f6(n) = 3n+1 + 5n4 Ja(n) 216 In(n) = ((9n2)(6n)(121))I/2 . An) = (4 + 5n + lg(n))l/2 g (n) +n lg(n) +500n 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. In other words, give a sequence fi, 2,... such that J(n)O(i+I(n)). Make a note if any two functions are asymptotically equivalent, i.e. if