I'm trying to determine a function $f(x)$ that is $O(f)$ but not $o(f)$ and also not $\Omega(f)$. Note the $f$ used in the asymptotic notation is not the same as $f(x)$.Originally I thought of $f(x)=\log(x), O(x)$ but I am not convinced that $o(x)$ is invalid for this function.Previously I thought it was, because I could always come up with some constant $c$ that would bring the function $x$ below $f(x)$. However, I could say the same for $o(2^x)$ because surely there is some infinitesimally small constant that I can find that will put $2^x$ below $f(x)$ at a given value $x$. Any advice in this matter?  
When can we assuredly say that a function is little o of some other function?
asymptotics;landau notation