A theorem named for this type of function is typically taught alongside the implicit function theorem because they provide similar tools for solving systems of equations. For 10 points each:
[10e] Name this type of function that “undoes” a given function and is often denoted with a superscript “minus one.”If g is this type of function for f, then f-of-g-of-x equals x.
ANSWER: inverse function
[10h] The inverse function theorem requires the invertibility of this construct. The sign of the determinant of this construct at a given point tells whether a continuously differentiable function changes orientation around that point.
ANSWER: Jacobian matrix
[10m] The elements of the Jacobian matrix are calculated via this operation. This operation gives the rate of change of a function with respect to one variable at a time.
ANSWER: partial derivative [prompt on derivative]
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