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inverse function theorem

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inverse function theorem [′in‚vərs ′fənk·shən ‚thir·əm]

(mathematics)

If ƒ is a continuously differentiable function of euclideann-space to itself and at a pointx₀the matrix with the entry (∂ƒ_i/∂x_j)_x₀in theith row andjth column is nonsingular, then there is a continuously differentiable functiong(y) defined in a neighborhood of ƒ(x₀) which is an inverse function for ƒ(x) at all points nearx₀.

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