My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum

Thanks Tree1Thanks
  • 1 Post By Maschke
LinkBack Thread Tools Display Modes
December 21st, 2017, 12:27 PM   #1
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.
Gigabitten is offline  
December 21st, 2017, 12:39 PM   #2
Math Team
Joined: Dec 2013
From: Colombia

Posts: 7,690
Thanks: 2669

Math Focus: Mainly analysis and algebra
Context dictates which solutions we take.
v8archie is offline  
December 21st, 2017, 02:52 PM   #3
Senior Member
Joined: Aug 2012

Posts: 2,410
Thanks: 754

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.
Maschke is offline  

  My Math Forum > High School Math Forum > Algebra

functions, noninvertible

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Derivatives, trignometric functions and exponential functions Nij Calculus 2 November 25th, 2015 06:20 AM
help with functions mustangman578 Algebra 4 May 31st, 2014 07:17 AM
Functions hoyy1kolko Algebra 1 January 7th, 2011 05:37 AM
Even and Odd Functions PokerKid Algebra 10 October 25th, 2008 08:39 AM
help / functions sel Calculus 3 October 21st, 2008 03:48 AM

Copyright © 2019 My Math Forum. All rights reserved.