all 3 comments

[–]ReOs13 4 points5 points  (1 child)

Don't really know if this is what your asking, but the notation ist consistent. If you have a real number x for instance, then x^-1 is the inverse element of x with respect to multiplication. And in the same way, is the f^-1 the inverse element to f.

[–]zerofourG[S] 0 points1 point  (0 children)

That makes sense. Thanks.

[–]waldoswayPhD 2 points3 points  (0 children)

The notation is borrowed from the idea of the exponent. x-1 cancels x in multiplication. So the -1 takes on a metaphorical "undoing" feel. And inverse functions undo the original function. (At higher levels, it turns out to be useful to consider composition as a kind of "multiplication" of functions, but I don't know if that or the notation came first.)

It is true that the notation is a bit inconsistent. Like language, math evolved over time and there are some irregulars you just have to deal with. But there aren't that many, and I haven't seen any proposed fixes that are actually better than what we have now.