My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum


Reply
 
LinkBack Thread Tools Display Modes
February 23rd, 2013, 10:24 AM   #1
Senior Member
 
Joined: Sep 2010
From: Germany

Posts: 153
Thanks: 0

inverse function of a multivariable function

could someone show me step by step how to find an inverse function of the following one...

rayman is offline  
 
February 23rd, 2013, 05:40 PM   #2
Member
 
Joined: Jan 2013

Posts: 93
Thanks: 0

Re: Inverse function of a multivariable function

There is no inverse. The function is not injective, e.g. .
Crimson Sunbird is offline  
February 23rd, 2013, 09:57 PM   #3
Senior Member
 
Joined: Sep 2010
From: Germany

Posts: 153
Thanks: 0

Re: inverse function of a multivariable function

well in my notes it actually is a bijective and cont fcn (thus a homeomorphism) between , they even give that inverse

but I have no clue how to find an inverse of a multivariable function
rayman is offline  
February 24th, 2013, 08:17 AM   #4
Member
 
Joined: Jan 2013

Posts: 93
Thanks: 0

Re: Inverse function of a multivariable function

Then you should have stated that the domain of your function is in the first place! If you donít state your question clearly, how are people going to understand your problem, let alone help you?

So, your function is from the circle ^2+y^2=1\}" /> to the square x|+|y|=1\}" />.

Draw a straight line from the origin making an angle () anticlockwise from the positive x-axis. This line intersects and at and respectively. What does is map the first point to the second point, so the inverse maps the second point to the first point. Itís just a matter of expressing the coordinates of the first point in terms of coordinates of the second point, really.

Let and . We want first to express in terms of and . Notice that . Hence



Similarly

Crimson Sunbird is offline  
Reply

  My Math Forum > College Math Forum > Real Analysis

Tags
function, inverse, multivariable



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Find all linear function given a function equals its inverse deSitter Algebra 4 April 10th, 2013 01:17 PM
find inverse of inverse function jaredbeach Algebra 1 November 17th, 2011 11:58 AM
Proving maximum of a certain multivariable function. Urgent! dgemu Calculus 0 February 7th, 2011 11:15 AM
Inverse function sphinn Algebra 8 September 23rd, 2010 11:28 PM
Implicitly Defined Multivariable Function Derivitives Schubatis1 Calculus 1 September 26th, 2008 08:13 PM





Copyright © 2017 My Math Forum. All rights reserved.