Kerning for function composition \circ f in math mode

I noticed that, in the many math fonts, the letter f looks asymmetrical when it is to the right of a binary operator. I think it is because the spacing is computed from the bottom tip of the f, instead of from the middle of the f.

In the following example, the first row the f is to the left of the operator and looks fine. In the second row the f is to the right and looks like the space between the circle and the f is too wide. In the third row I kludged with a negative \! space before the f; it looks better but perhaps a bit too narrow.

As mentioned, the best workaround I could find is to manually add a \! before every single f. Is there a more robust or accurate way to fix this? I presume I must not be the first one to run into this issue where the function composition operator looks wonky when one of the functions is named f...

\documentclass{article} \begin{document} Hello $f \circ g$. Hello $g \circ f$. Hello $g \circ \! f$. \end{document}