(6 points)Define the function f(x, y) = (xy, x + y) on R. (a) (3 point)...

 

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(6 points)Define the function f(x, y) = (xy, x + y) on R. (a) (3 point) Determine on which set of points in R2 the hypotheses of the inverse function theorem is satisfied. (b) (3 points) Apply the inverse function theorem to f at the point (2, 1) and use it to find Dg(2,5) where g is a local inverse for f at the point (2, 1). (6 points)Define the function f(x, y) = (xy, x + y) on R. (a) (3 point) Determine on which set of points in R2 the hypotheses of the inverse function theorem is satisfied. (b) (3 points) Apply the inverse function theorem to f at the point (2, 1) and use it to find Dg(2,5) where g is a local inverse for f at the point (2, 1).