Time complexity of a function that i dont think could even exist

Question

So i got this question in the exam, Find the time complexity of the function

logn+3nlogn-100n^2+50

All logs have base 2

Can anyone tell if the answer is nlogn or n^2 even though I doubt such a function could even exist for an algorithm.

Answer 1

Yes, you are right that such complexity function would never exist since after a certain value of n, your function is always negative(due to -100n^2), which is not possible. Still if someone asks you the complexity of such a function it should be answered to be O(n^2).