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April 5th, 2017, 10:26 AM  #1 
Member Joined: Nov 2016 From: Kansas Posts: 70 Thanks: 0  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: 1,329 Thanks: 94 
i) Solve for x & y. g(x,y) = 10 say. ii) sin(x+2pi)=sinx iii) 0<x<1, 0<y<pi/2 

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global, invertibility, local 
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