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Mathematica > Mathematics and Algorithms > Mathematical Functions > Special Functions > Inverse Functions >

Built-in Mathematica Symbol

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.

InverseFunction[f, n, tot]
represents the inverse with respect to the n

argument when there are tot arguments in all.

As discussed in Functions That Do Not Have Unique Values, many mathematical functions do not have unique inverses. In such cases, InverseFunction[f] can represent only one of the possible inverses for f.

InverseFunction is generated by Solve when the option InverseFunctions is set to Automatic or True.

The "inverse function" of Sin is ArcSin:

Symbolic inverse function:

Derivative of an inverse function:

The "inverse function" of Sin is ArcSin:

Symbolic inverse function:

Derivative of an inverse function: