InverseFunctions

InverseFunctions

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

Details

  • Settings for InverseFunctions are:
  • Truealways use inverse functions
    Automaticuse inverse functions, printing a warning message (default)
    Falsenever 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 InverseFunction[f] 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:

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

With InverseFunctions->True, Solve does not print inverse function warning messages:

Symbolic inverses are used for all symbols:

With InverseFunctions->False, Solve does not use inverse functions:

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

Solving algebraic equations does not require using inverse functions:

Wolfram Research (1991), InverseFunctions, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseFunctions.html.

Text

Wolfram Research (1991), InverseFunctions, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseFunctions.html.

CMS

Wolfram Language. 1991. "InverseFunctions." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseFunctions.html.

APA

Wolfram Language. (1991). InverseFunctions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseFunctions.html

BibTeX

@misc{reference.wolfram_2024_inversefunctions, author="Wolfram Research", title="{InverseFunctions}", year="1991", howpublished="\url{https://reference.wolfram.com/language/ref/InverseFunctions.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_inversefunctions, organization={Wolfram Research}, title={InverseFunctions}, year={1991}, url={https://reference.wolfram.com/language/ref/InverseFunctions.html}, note=[Accessed: 21-December-2024 ]}