About the ambiguity: If I write f^{-1}(x), without context, you have literally no way of knowing whether I am talking about a multiplicative or a functional inverse, which means that it is ambiguous. It’s correct notation in both cases, used since forever, but you need to explicitly disambiguate if you want to use it.
I hope this helps you more than the stackexchange post?
If I write f^{-1}(x), without context, you have literally no way of knowing whether I am talking about a multiplicative or a functional inverse, which means that it is ambiguous
The inverse of the function is f(x)^-1. i.e. the negative exponent applies to the whole function, not just the x (since f(x) is a single term).
We’ve been at this point, I’m not going to explain this again. But you weren’t able to read a single sentence of a wikipedia article without me handfeeding it to you, so I guess I shouldn’t be surprised. I’m sorry for your students.
About the ambiguity: If I write
f^{-1}(x), without context, you have literally no way of knowing whether I am talking about a multiplicative or a functional inverse, which means that it is ambiguous. It’s correct notation in both cases, used since forever, but you need to explicitly disambiguate if you want to use it.I hope this helps you more than the stackexchange post?
The inverse of the function is f(x)^-1. i.e. the negative exponent applies to the whole function, not just the x (since f(x) is a single term).
You can define your notation that way if youlike to, doesn’t change the fact that commonly
f^{-1}(x)is and has been used that way forever.If I read this somewhere, without knowing the conventions the author uses, it’s ambiguous
Nothing to do with me - it’s in Maths textbooks.
Well they should all be following the rules of Maths, without needing to have that stated.
Exactly! It’s in math textbooks, in both ways! Ambiguous notation, one might say.
And both ways are explained, so not ambiguous which is which.
Yeah, doesn’t mean that you know what an author is talking about when you encounter it doing actual math
The notation is not intrinsically clear, as any human writing. Ambiguous, one may say.
It is to me, I actually teach how to write it.
We’ve been at this point, I’m not going to explain this again. But you weren’t able to read a single sentence of a wikipedia article without me handfeeding it to you, so I guess I shouldn’t be surprised. I’m sorry for your students.