An inverse function is a concept of mathematics. A function will calculate some output , given some input . This is usually written . The inverse function does the reverse. Let's say is the inverse function of , then . Or otherwise put, . An inverse function to is usually called . [1] It is not to be confused with , which is a reciprocal function.

In calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the derivative of f. More precisely, if the inverse of f {\displaystyle f} is denoted as f − 1 {\displaystyle f^{-1}} , where f − 1 ( y ) = x {\displaystyle f^{-1}(y)=x} if and only if f ( x ) = y {\displaystyle f(x)=y} , then the inverse function rule is, in …

In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, [1] [2] [3] [4] [5] antitrigonometric functions [6] or cyclometric functions [7] [8] [9]) are the inverse functions of the trigonometric functions (with suitably restricted domains ).

Notation. The ISO 80000-2 standard abbreviations consist of ar-followed by the abbreviation of the corresponding hyperbolic function (e.g., arsinh, arcosh). The prefix arc-followed by the corresponding hyperbolic function (e.g., arcsinh, arccosh) is also commonly seen, by analogy with the nomenclature for inverse trigonometric functions.These are misnomers, since the prefix …

In mathematics, integrals of inverse functions can be computed by means of a formula that expresses the antiderivatives of the inverse f − 1 {\displaystyle f^{-1}} of a continuous and invertible function f {\displaystyle f}, in terms of f − 1 {\displaystyle f^{-1}} and an antiderivative of f {\displaystyle f}. This formula was published in 1905 by Charles-Ange Laisant.

Inverse Functions If a function is one-to-one, then to each y in the range of f there is a unique x in the domain that maps on top of it. So we can define a function from the range of f back to the domain. This new function is called the inverse function, and is denoted . Properties: Let f be a one-to-one function, and be its inverse.

Inverse function, a function that "reverses" another function Generalized inverse, a matrix that has some properties of the inverse matrix but not necessarily all of them; Multiplicative inverse (reciprocal), a number which when multiplied by a given number yields the multiplicative identity, 1 Inverse matrix of an Invertible matrix; Other uses. Invert level, the base interior level of a pipe, …

Its inverse function is the natural logarithm, denoted [nb 1] [nb 2] or because of this, some old texts [3] refer to the exponential function as the antilogarithm . Contents 1 Graph 2 Relation to more general exponential functions 3 Formal definition 4 Overview 5 Derivatives and differential equations 6 Continued fractions for ex 7 Complex plane