Does $f \in o(g)$ imply $g^{-1} \in o(f^{-1})$?
Solution 1:
No. For example, take $f(x) = e^x$ and $g(x) = e^{2x}$, so that $g^{-1}(x) = \frac12\log x$ and $f^{-1}(x) = \log x$.
Does $f \in o(g)$ imply $g^{-1} \in o(f^{-1})$?
Solution 1:
No. For example, take $f(x) = e^x$ and $g(x) = e^{2x}$, so that $g^{-1}(x) = \frac12\log x$ and $f^{-1}(x) = \log x$.