Which pair of functions satisfy f (N) ~g(N)?

Question

I\'ve just started working with algorithms and I am doing some tasks like this question:

I think, the right answer is A. As the functions are the same, or do I miss some

Answer 1

Yes, A is the correct answer.

Tilde here means an (approximate, not precise) equivalence relation. Or in other words, the limit of f(N) / g(N) as N approaches infinity = 1.

In answer A, f and g are obviously equivalent, so the limit is 1. This doesn't hold for the other three answers, which have limits 3, 0, and 3 respectively.