Giving the Big O, Big Theta and Big Omega for a function

Question

How can one give Big O, Big Theta or Big Omega for a function like

T(n) = n + 10*log n

Can someone please tell me how I can get the complexity for such a thing?

Answer 1

Drop all lower-order terms and constants and you get:

Θ(T(n)) = Θ(n + 10*log(n)) = Θ(n)

Since this is a tight bound (Θ) we also infer upper and lower bounds as O(n) and Ω(n).