Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Discrete mathematics, continuous mathematics, and probability / 3 / a

For these real-valued functions, $f(n)=O(g(n))$ means that there exist constants $C>0$ and $N\in \mathbb{N}$ such thatThe absolute values matter because neither function is assumed nonnegative. The constants are independent of $n$; finitely many earlier values do not affect Big O notation.