I mainly need an answer to part B. Please do not find someone elses solution on th internet and use it. Also, for part b, prove by finding c (constant) and n0.

Problem 5. a. Rank the following functions by order of growth, that is, find an arrangement g1,g2,... of the functions satisfying gi 20g2), g2 2(g3), Partition your list into equivalence classes such that n) and g(n) are in the same class if and only if f(n) O(g(n lg n n ig n 21g m (n 1)! b. Give an example of a single non-negative function f (n) such that for all functions gi(n) in part (a) f (n) is neither O(gi(Ta)) nor 2(gi (m))