Are you talking about the common representation of the function y=f(x)? It can be considered as a code name of the function or a code name of the corresponding rule of the function. It's actually a name. You don't have to use f, such as g, h and so on.

For example: f (x) = 2x+ 1 (x < 5), it can be considered that f is the corresponding rule 2x+ 1, x.

F is taken from the word function in the west. In English, function is the word function.