• InverseFunctions is an option for Solve and related functions which specifies whether inverse functions should be used.
• Settings for InverseFunctions are:
|True ||always use inverse functions |
|Automatic ||use inverse functions, printing a warning message (default) |
|False ||never use inverse functions |
• 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
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.
• New in Version 2.