Let ECR be an open set and let f:ER be Continuously differentiable. Suppose further there exists...

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Let ECR² be an open set and let f:ER be Continuously differentiable. Suppose further there exists (x, y) EE such that af (xo, yo) #0 ax Prove that is not injective. Hint: If G" (u, v) = (4(u, v), y(u, v)) is the inverse of G obtained for (u, v) in an Open set Containing (Uo, Vo) = G(xo, y₂), write out and analyze the condition (GoG") (UV) = (u, v) Let ECR² be an open set and let f:ER be Continuously differentiable. Suppose further there exists (x, y) EE such that af (xo, yo) #0 ax Prove that is not injective. Hint: If G" (u, v) = (4(u, v), y(u, v)) is the inverse of G obtained for (u, v) in an Open set Containing (Uo, Vo) = G(xo, y₂), write out and analyze the condition (GoG") (UV) = (u, v)