What are Reciprocal Functions?

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x^-1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution).

The notation f^-1 is sometimes also used for the inverse function of the function f, which is not in general equal to the multiplicative inverse. For example, the multiplicative inverse 1/(sin x) = (sin x)^-1 is the cosecant of x, and not the inverse sine of x denoted by sin^-1 x or arcsin x.¹

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