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April 5th, 2017, 10:26 AM   #1
ZMD
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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.
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April 12th, 2017, 07:21 AM   #2
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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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