Question

If f(x) = 3x^2 + x^3logx, then f(x) is?

(a) O(x^2)

(b) O(x^3)

(c) O(x)

(d) O(1)

The question was asked in exam.

My doubt is from The Growth of Functions topic in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

Right choice is (b) O(x^3)

For explanation: 0 < 3x^2 <  x^3, it follows that 0 < 3x^2 + x^3logx <  x^3. Consequently, f(x) = O(x^3).