Hi all
I'm probably missing something, it's not obvious that g(n) = O(f(n)) for all n (I don't see how 2^1000 boundaries of g(n) make any different here) ?
Yes, $\displaystyle g(n)=O(f(n))$, but is that what the question is asking for? The wording seems pretty obscure.
Could it want something like: $\displaystyle f(n)=O(n^3\log(n))$ and $\displaystyle g(n)=O(n^3)$ and so $\displaystyle g(n)=O(n^3\log(n))$.
Also you probably are expected to justify $\displaystyle f(n)=O(n^3\log(n))$
CB