Q7. [10 pts] Grouping Functions by Complexity Category a. [6 pts] Group the following functions by complexity category and sort the identified categories in decreasing complexity order by giving enough justifications to your solution: 8n + 12, n3/2, n, 2", n1/100, n, 5n2 + 7n, log (n!), n!, nlog n, n2, 2n!, n+ n log n, (log n)? b. [2 pts] The function f(x) = (log n)2 + 2n + 4n + log n + 50 belongs in which of the following complexity categories: (a) e(Ign) (b) ((log n)) (c) P(n) (d) O(n lg n) (e) O(n(lg n)2) (f) None of these C. [2 pts] The function f(x) = f(x) = n + n + 2n + n4 belongs in which of the following complexity categories: (a) O(n) (b) 0(na) (c) 6(n) (d) O(n lg n) (e) O(n^) (f) None of these