This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 InverseFunction InverseFunction[ f ] represents the inverse of the function f, defined so that InverseFunction[ f ][ y ] gives the value of x for which f [ x ] is equal to y. For a function with several arguments, InverseFunction[ f ] represents the inverse with respect to the first argument. InverseFunction[ f , n ] represents the inverse with respect to the n argument. InverseFunction[ f , n , tot ] represents the inverse with respect to the n argument when there are tot arguments in all. In OutputForm and StandardForm, InverseFunction[ f ] is printed as . As discussed in Section 3.2.7, many mathematical functions do not have unique inverses. In such cases, InverseFunction[ f ] can represent only one of the possible inverses for f. Example: InverseFunction[Sin]. InverseFunction is generated by Solve when the option InverseFunctions is set to Automatic or True. See the Mathematica book: Section 2.2.1, Section 2.2.9, Section 3.4.5. See also: Solve, InverseSeries, Composition, Derivative. Further Examples Here are two inverse functions evaluated at y. In[1]:= Out[1]= In[2]:= Out[2]= Composing a function with its inverse in either order is the identity operation. In[3]:= InverseFunction::ifun: Warning: Inverse functions are being used. Values may be lost for multivalued inverses. Out[3]= In[4]:= InverseFunction::ifun: Warning: Inverse functions are being used. Values may be lost for multivalued inverses. Out[4]= The inverse of a composition is another composition. In[5]:= Out[5]=