Problem 1. Order the following functions by asymptotic dominance. That is, give an ordering f1, f2, ..., such that for all i > 1, we have fi(n) = O(fi+1(n)). f(n) = 2". f(n) = 1000. n. f(n) = nlogn f(n) = n2. f(n) = 22". f(n) = log(n). f(n) = log(log(n)). f(n) = n log(n)