\b[False.] On every odd positive <integer> $n$, $f(n)/g(n)=n$. Given any proposed <Big O notation> constant $C$ and threshold $N$, choose an odd $n>\max(C,N)$. Then $f(n)>Cg(n)$, contradicting the required bound. The behavior on even <integers> cannot repair this failure on an unbounded <subsequence>.

Solution

Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Discrete mathematics, continuous mathematics, and probability resit / 3 / a / v / Solution

 Solution (source code)