Talk:Inverse function

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[edit] 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)

[edit] 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?

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

[edit] 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).