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April 24th, 2012, 12:14 AM   #1
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Let U denote the right half plane {(u,v)?R^2 ?u>0}

Let U denote the right half plane {(u,v)?R^2 ?u>0}. Define a function H: U -> R^2 by

H(u,v) = (ue^-v , ue^v)

a.Let Q denote the range of H. Show that Q = {(x,y) ?R^2 ?x>0,y>0}, the first quadrant
b.Find H^ -1 on Q
c.Compute DH and D(H^ -1)
d.Show that DH and D(H^ -1) are inverse to one another
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