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This article needs to be split in two in some way
This article needs to be split in two in some way.
Method 1: Split this article into two articles in the Wikipedia.
Method 2: Split this article into two large nonoverlapping sections. Call them Part A and Parr B for the moment.
In either case, Part A will be all about functions of just one real number and their inverse functions. The functions themselves will only have real numbers in their ranges.
In either case, Part B will cover functions and mappings of a lot more generality. The objects in the domains and ranges of the functions can be abstract "points" in the two sets, or to be more specific, pairs of real numbers in both sets, triples of real numbers, complex numbers, quaternions, or functions themselves - whatever you like.
Hence Part A will be strictly on the level of high school students and lower-level college freshmen. Then Part B will be for readers with more background and interest in math, incluing those who have studied multivarible calculus, complex analysis, and whatever.
This ought to cut down on a lot of confusion and arguments - especially concerning people who know something about Part A, but them they want to get argumentative about things in Part B, which is a lot more generalized.
See also the article on the Inverse Function Theorem for some guidance.
22.214.171.124 (talk) 08:25, 4 August 2012 (UTC)
"undoes" another function ?
I think this is really very bad terminology. So "log" undoes "exp"? Then how comes that the function exp still exists, since log undid it? One function cannot undo another function, at best, it can undo (sic) the "action" of the other function.
PS: "putting y into the (...) function g " is roughly as bad. Since when are we putting things into a function? C'mon, there's a difference between being understandable and using baby language, esp. in an article about mathematics...
PS2: "Direct variation function are based on multiplication; y = kx. The opposite operation of multiplication is division and an inverse variation function is y = k/x." --- nonsense! (and bad grammar...) The second function does not divide x by k, as opposed to the first which multiplies x by k. (If you are "putting" kx "into" the 2nd function, you get y=1/x!) Maybe the author should first stick to addition, with y=x+a (aka "translation"), then the inverse operation obviously is y=x-a, and not a-x). — MFH:Talk 04:58, 9 September 2012 (UTC)
- The lead paragraph: I agree that the first sentence is not as clear as it could be, although I think you're making a bigger deal out of the difference between a function and its effect than is really warranted. Changing "undoes another function" to "undoes the effect of another function" or "undoes the action of another function" would probably better. Perhaps it would be better to put the rigorous definition first and then put this sentence, making it clear that it's an intuitive point of view. But in that case the rigorous definition should be expressed in words instead of symbols, in my view. Either way, it should be corrected - at the moment it only defines a one-sided inverse! Quietbritishjim (talk) 16:25, 9 September 2012 (UTC)
Inverses in calculus
"Inverses in calculus" should refer to the Fundamental Theorem of the Calculus because the fact that integration and differentiation are the inverse operations of each other is waht the relationship between differential calculus and integral calculus is all about.
If Isaac Newton and Gottfried Wilhelm von Leibnitz had not discovered the Fundamental Theorem of the Calculus (of something simpler than it), then we would be in serious trouble in science, technology, and mathematics. Not even mentioning the Fundamental Theorem of the Calculus is a serious lacking.
This article also has other serious problems. I suggest that it needs to be scrapped and redone from scratch.
126.96.36.199 (talk) 23:37, 19 September 2012 (UTC)
some of it could be simpler, is this the simple English Wikipedia. For example I have just learnt that a way to think of the inverse of a number is 1 divided by that number. Rather than that number divided by 1. So this clearly says what is inverted. The mathematical explanations do not say that in written English. This inappropriate writing style (as found here) give the problems in understanding mathematics. — Preceding unsigned comment added by 188.8.131.52 (talk) 14:20, 15 January 2013 (UTC)
Definition. * is an operation on A, i.e. a*x =b where a, x, b are at A, then x = a-1*b, if * is conmutative, we can write x = b*a-1; else x = bºa; at this case º is named inverse operation of *.--184.108.40.206 (talk) 17:42, 26 April 2013 (UTC)
- There is a detailed discussion in inverse function #Partial inverses. The last paragraph of inverse function #Definitions also consider this. Note that section levels currently appear to be broken, with “examples” sections following “Definitions” as ===s (subsections) for no reason; I refer to the last paragraph of “Definitions” proper. Incnis Mrsi (talk) 11:35, 4 January 2014 (UTC)