= = 2 > 38. Let f: R2 + R2 be given by f(x, y) = (x2 + y2, x2 - y2), for all (x,y) € R2. Calculate J(f)(x,y) and describ

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2 38 Let F R2 R2 Be Given By F X Y X2 Y2 X2 Y2 For All X Y R2 Calculate J F X Y And Describ 1 (173.05 KiB) Viewed 31 times

= = 2 > 38. Let f: R2 + R2 be given by f(x, y) = (x2 + y2, x2 - y2), for all (x,y) € R2. Calculate J(f)(x,y) and describe the set A = {(x,y): J(f)(x,y) = 0}, illustrating by means of a pic- ture. If (xo, yo) ¢ A, deduce from the Inverse Function Theorem that f has an inverse near (20, yo), calculate explicitly what it is, and calculate (f-1)'(f(x0, yo)). Show that (1,-1) € A and calculate (F-1)'(2,0). -