Suppose I have a function $f$ and derive another function from it with similar properties. For example I have that my new function is zero when the other function is zero.
I would still like to use the same letter for the new function. I could for example for something like $\dot f$ or $\breve f$, but I probably need another symbol above the $f$.
What symbol is normally used to denote that we have a function which is equivalent to a given $f$ in some respects?
There isn't a single fixed symbol, but it's common to use $\tilde{f}$ or $\overline{f}$ in such cases (e.g., for extensions of a given function $f$).