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RootRoots

InverseFunctions

FilledSmallSquareInverseFunctions is an option for Solve and related functions which specifies whether inverse functions should be used.

FilledSmallSquare Settings for InverseFunctions are:

FilledSmallSquare Example: Solve[f[x] == a, x, InverseFunctions->True] LongRightArrow.

FilledSmallSquare Inverse functions provide a way to get some, but not in general all, solutions to equations that involve functions which are more complicated than polynomials.

FilledSmallSquareSolve[Sin[x] == a, x, InverseFunctions->True] LongRightArrow gives a single solution in terms of ArcSin. In fact, there is an infinite number of solutions to the equation, differing by arbitrary multiples of . Solve gives only one of these solutions.

FilledSmallSquare When there are several simultaneous equations to be solved in terms of inverse functions, Solve may fail to find any solutions, even when one exists.

FilledSmallSquare When inverse functions are allowed, Solve solves for f[expr] first, then applies InverseFunction[f] to the result, equates it to expr, and continues trying to solve for the remainder of the variables.

FilledSmallSquare See The Mathematica Book: Section 3.4.5.

FilledSmallSquare See also: FindRoot.

Further Examples

RootRoots