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Relations with other functions


With inverse function

This property is the definition of the inverse function and can hold without additional restrictions on (like , where is not ) for many named functions. In these situations, is in most cases free of branch cuts. For example, ; here means with , that is, the inverse sine function (do not confuse this with the reciprocal function ).

Some of the functions are invertible: their inversions can coincide with the original , but for other values of the parameters. For example, the inverse function for the power function is also the power function , and the relation takes place only under the restriction . In general cases the following relation takes place: .

The last property for the inverse function of the direct function can be valid under special restrictions for (where typically is not ). For example,