Asymptotic Notation: Does f in o(g) imply g not in O(f)?

Question

Does $f \in o(g)$ imply $g \not\in O(f)$?

Thank you very much for your help!

Answer 1

Try for instance $f(x)=\ln x$ and $g(x)=x$. Then $f\in o(g)$. But $g\not\in O(f)$.

In general, if $g$ grows faster than $f$, then $g/f$ will "blow up".