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-   -   Noninvertible* Functions (http://mymathforum.com/algebra/343120-noninvertible-functions.html)

Gigabitten December 21st, 2017 12:27 PM

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?

v8archie December 21st, 2017 12:39 PM

Context dictates which solutions we take.

Maschke December 21st, 2017 02:52 PM

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.


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