inverse function theorem


inverse function theorem

[′in‚vərs ′fənk·shən ‚thir·əm] (mathematics) If ƒ is a continuously differentiable function of euclidean n-space to itself and at a point x0 the matrix with the entry (∂ƒi /∂ xj )x0in the i th row and j th column is nonsingular, then there is a continuously differentiable function g (y) defined in a neighborhood of ƒ(x0) which is an inverse function for ƒ(x) at all points near x0.