I have trouble figuring out the asymptotic behavior of two functions.
If $f(n) = n \log n$, then what do we know about $f^{-1}(n)$? I.e. what is the asymptotic behavior of $g(n)$ such that $g(n) \log(g(n)) = \Theta(n)$, perhaps in terms of some familiar functions?
Behavior of $n^{\frac{1}{\log \log n}}$. I know that $n^{\frac{1}{\log n}} = e$, so this function would be super-constant. But what is known about its asymptotic behavior?