Question

The big-theta notation for f(n) = nlog(n^2 + 1) + n^2logn is?

(a) n^2logn

(b) n^2

(c) logn

(d) nlog(n^2)

The question was asked in class test.

Question is from The Growth of Functions in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

Correct answer is (a) n^2logn

Easy explanation: n^2logn < n^3, it follows that nlog(n^2 + 1) + n^2logn is less than n^3 and greater than  n^2logn.