I would like to know if it is possible that two functions $f(n), g(n)$ can exist such that both of the following conditions are met:
$g(n) = o(1)$
$f(n-g(n)) \neq \Theta (f(n))$
I though I found $1/n$ and $1/n^2$ but I think I got it all wrong.
Is it even possible?!