Question

The big-O notation for f(n) = (nlogn + n^2)(n^3 + 2) is?

(a) O(n^2)

(b) O(3^n)

(c) O(n^4)

(d) O(n^5)

This question was posed to me by my school teacher while I was bunking the class.

This key question is from The Growth of Functions in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

Correct option is (d) O(n^5)

The explanation: 0 < n^3 + 2 < n^3, it follows that (nlogn + n^2)(n^3 + 2) is less than equal to n^5.