Question: Let f: S n be a differentiable function on a convex set S n. Suppose that the Jacobian Jf(x) is positive (or negative)

Let f: S → ℜn be a differentiable function on a convex set S ⊆ ℜn. Suppose that the Jacobian Jf(x) is positive (or negative) definite for all x ∈ S. Then f is one-to-one.

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