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 Documentation / Mathematica / Built-in Functions / Algebraic Computation / Equation Solving  /
InverseFunctions

  • InverseFunctions is an option for Solve and related functions which specifies whether inverse functions should be used.
  • Settings for InverseFunctions are:
  • Example: Solve[f[x] == a, x, InverseFunctions->True].
  • 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[Sin[x] == a, x, InverseFunctions->True] 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.
  • 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.
  • See the Mathematica book: Section 3.4.5.
  • See also: FindRoot.

    Further Examples

    With the default option setting InverseFunctions -> True, Solve will attempt to solve some equations that involve other functions.

    In[1]:=

    Out[1]=

    In[2]:=

    InverseFunction::ifun: Warning: Inverse functions are being used. Values may be lost for multivalued inverses.

    Out[2]=

    Setting InverseFunctions -> False, however, tells Mathematica not to make any assumptions about the function being solved.

    In[3]:=

    InverseFunction::ifun: Warning: Inverse functions are being used. Values may be lost for multivalued inverses.

    Solve::tdep: The equations appear to involve transcendental functions of the variables in an essentially non-algebraic way.

    Out[3]=