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 and Section 3.4.5.
See also: Solve, InverseSeries, Composition, Derivative.