My Math Forum Noninvertible* Functions

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 December 21st, 2017, 12:27 PM #1 Newbie   Joined: Nov 2013 Posts: 6 Thanks: 0 Noninvertible* Functions I've noticed that the inverse of f(x)=x^2 is NOT itself a function, but can still be described as f(-1)(x)=+/-sqrt(x). More or less, f(-1)(x)=sqrt(x)&-sqrt(x). Is there a name for situations like this, where the inverse of a function isn't a function itself but is a concatenation of functions? What about cases like the inverse of cosine, where the answer is more of an infinite family of answers than a single answer? Last edited by Gigabitten; December 21st, 2017 at 12:30 PM.
 December 21st, 2017, 12:39 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,663 Thanks: 2642 Math Focus: Mainly analysis and algebra Context dictates which solutions we take.
 December 21st, 2017, 02:52 PM #3 Senior Member   Joined: Aug 2012 Posts: 2,321 Thanks: 714 In complex analysis there's a thing called a Riemann surface in which all the possible inverse values are taken as a single geometric structure. The Wiki article has some nice pictures of the Riemann surface for $\sqrt{z}$ and other familiar functions in which you can see what's going on. Thanks from greg1313 Last edited by Maschke; December 21st, 2017 at 03:16 PM.

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