# InverseFunctions

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

# Details • Settings for InverseFunctions are:
•  True always use inverse functions Automatic use inverse functions, printing a warning message (default) False never use inverse functions
• 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.
• Solve[x+E^x==a,x,InverseFunctions->True]{{x->a-ProductLog[E^a]}} gives a single solution in terms of ProductLog. In fact, there is an infinite number of solutions to the equation, corresponding to different branches of ProductLog. Solve gives only one of these solutions.
• 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.
• When inverse functions are allowed, Solve solves for f[expr] first, then applies to the result, equates it to expr, and continues trying to solve for the remainder of the variables.

# Examples

## Basic Examples(3)

By default, Solve uses inverse functions but prints warning messages:

 In:=  Out= In:=  Out= For symbols with the NumericFunction attribute, symbolic inverses are not used:

 In:=  Out= With , Solve does not print inverse function warning messages:

 In:= Out= In:= Out= Symbolic inverses are used for all symbols:

 In:= Out= With , Solve does not use inverse functions:

 In:=  Out= Here, a method based on Reduce is used, as it does not require using inverse functions:

 In:= Out= Solving algebraic equations does not require using inverse functions:

 In:= Out= Introduced in 1991
(2.0)