
Real Analysis Real Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 5th, 2017, 10:26 AM  #1 
Member Joined: Nov 2016 From: Kansas Posts: 73 Thanks: 1  Local and Global Invertibility
Let g:$R^{2}\ > R^{2}$ be defined by g(x,y):=\begin{pmatrix} e^{x}cos(y)\\ e^{x}sin(y) \end{pmatrix} (i)Show that g is everywhere locally invertible; (ii)Show that g is not injective; (iii)Determine an open subset U ⊂ $R^{2}$ on which g is injective. Last edited by ZMD; April 5th, 2017 at 10:31 AM. 
April 12th, 2017, 07:21 AM  #2 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,364 Thanks: 100 
i) Solve for x & y. g(x,y) = 10 say. ii) sin(x+2pi)=sinx iii) 0<x<1, 0<y<pi/2 

Tags 
global, invertibility, local 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Local Minima and Local Maxima  life24  Calculus  7  May 16th, 2016 03:34 PM 
local invertibility does not imply global invertibility  JWS  Calculus  3  May 14th, 2014 11:10 PM 
Proof of invertibility  restin84  Number Theory  3  April 26th, 2012 12:14 PM 
Invertibility  mia6  Linear Algebra  2  December 19th, 2010 02:12 PM 
invertibility  tinynerdi  Linear Algebra  2  February 20th, 2010 05:33 PM 