My Math Forum (http://mymathforum.com/math-forums.php)
-   Algebra (http://mymathforum.com/algebra/)
-   -   Noninvertible* Functions (http://mymathforum.com/algebra/343120-noninvertible-functions.html)

 Gigabitten December 21st, 2017 01:27 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 01:39 PM

Context dictates which solutions we take.

 Maschke December 21st, 2017 03:52 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.

 All times are GMT -8. The time now is 10:09 AM.