Talk:Inverse function/Archive 1

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This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Contents 1 Inverse function theorem 2 Is the inverse of a function ever equal to that function to the power minus one? 3 Definition is incorrect 4 Existence of an inverse 5 Equivalent definitions 6 Left and right inverses, and Equivalent definitions

Inverse function theorem

"For functions between Euclidean spaces, the inverse function theorem gives a sufficient and necessary condition for the inverse to exist."

I don't see why the Inverse function theorem is a necessary condition for the inverse to exist. (I've found the same claim on page PlanetMath.) Mozó 18:04, 9 October 2006 (UTC)

Is the inverse of a function ever equal to that function to the power minus one?

Simple question (perhaps badly phrased in the title): is f^-1 (x) = (f(x))^-1 ever true? In case I've written that wrong, that is to say that if f(x) is some function of x, g(x) is that function to the power minus one, and is also the inverse of f(x). I realise that f^-1 (x) does not indicate (f(x))^-1 usually, which can be confusing with trigonometric functions, but could it ever be the same thing?

So g(x) = 1/f(x) = f^-1(x) which implies that the functional inverse of 1/f(x) equals f(x). What you're asking, essentially, is if the multiplicative inverse has an inverse function. In fact, it is its own inverse. 59.112.51.89 19:36, 27 April 2007 (UTC)

Yes: { (1,1) } is such a function. manczura@ccccd.edu

Definition is incorrect

The definition is incorrect as X is not necessarily the domain of f^{-1}. —The preceding unsigned comment was added by 24.94.246.41 (talk) 22:35, 9 February 2007 (UTC).

Existence of an inverse

Why must f be bijective? Shouldn't it be enough for f to be injective?

Equivalent definitions

The "equivalent definition" (that is obvious in the first place) is now really excessive. I propose to revert a bit. Sam Staton 09:09, 6 September 2007 (UTC)

It is obvious only for those who know the notation used, and I believe that most readers know the notation f(x), but much less readers know function composition and symbolic logic. However, I only tried to interpret Wahrmund's suggestion (see his 5 September edit) in such a way as to avoid his equations with three members. See if you like the shorter version that I edited a few minutes ago. Paolo.dL 10:07, 6 September 2007 (UTC)

Left and right inverses, and Equivalent definitions

User:Wahrmund, you reverted my edits to the section on left and right inverses. Was it intentional -- can you explain? Otherwise I will redo them. I see you also undid a sensible edit by User:Paolo.dL. Why? Sam Staton 09:51, 7 September 2007 (UTC)

User:Wahrmund, I am sure you did that unintentionally, but yesterday by copying and pasting a long block of old text you destroied many of my recent edits in different sections of the article. As you see in the "history" page associated with this article (just click on the tag at the top of the page), I provide the reason of each of my edits separately and carefully. Please see my "edit summaries" in the history page before undoing them. Please edit different sections separately (by clicking the respective "edit" link), and explain each change separately in the relevant edit summary, or in this talk page. Thanks, Paolo.dL 10:04, 7 September 2007 (UTC)

User:Sam Staton This has to be a software malfunction. My last edit was confined exclsuviely to "Equivalent definitions". I made absolutely NO changes to Left and Right Inverses. I didn't even read it. And I never cut-and-paste long blocks of text. Please let me know which Paolo.dL edit you are referring to, as I think there were several of these. Then I will attempt to address the issue. FYI, I will be out of the country and unavailable from Sept. 12 to Oct. 10. Morris K. 01:20, 8 September 2007 (UTC)

Morris, please see this comparison between your latest edit and a previous version of the article. It appears evident that you opened an old version (by means of the history page), then you edited that old version and saved it, ignoring the following two warnings appearing (within frames with orange background) immediately above the editing window:

This is an old revision of this page, as edited by Paolo.dL at 08:49, 6 Sept 2007. It may differ significantly from the current revision.
You are editing an old revision of this page. If you save it, any changes made since then will be removed.

Please carefully read these warnings. Any other hypothesis about what happened is, in my opinion, almost as unlikely as the occurrence described by the infinite monkey theorem. I perfectly know that a newbie, when passionately editing an article, may not see warnings (something similar happened to me some time ago), but actually your single click on that "Save page" button was sufficient to remove from the article 13 changes done after 08:49, 6 September 2007! And they included 4 edits by Sam Staton and 9 by me! That's a lot of work. Please never do that again, unless you really want to delete all changes made after a given date and time. Thanks, Paolo.dL 13:13, 9 September 2007 (UTC)

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.