mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if...

mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, cyclometric, or arcus functions) are the inverse functions of the...

specifically differential calculus, the inverse function theorem gives a sufficient condition for a function to be invertible in a neighborhood of a point...

mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. There are six 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...

In mathematics, the inverse gamma function Γ − 1 ( x ) {\displaystyle \Gamma ^{-1}(x)} is the inverse function of the gamma function. In other words, y...

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)...

In economics, an inverse demand function is the mathematical relationship that expresses price as a function of quantity demanded (it is therefore also...

percentile function (after the percentile), percent-point function, inverse cumulative distribution function (after the cumulative distribution function or c...

considered above grows very rapidly, its inverse function, f−1, grows very slowly. This inverse Ackermann function f−1 is usually denoted by α. In fact,...

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}}...

from any probability distribution given its cumulative distribution function. Inverse transformation sampling takes uniform samples of a number u {\displaystyle...

mathematics, an involution, involutory function, or self-inverse function is a function f that is its own inverse, f(f(x)) = x for all x in the domain of...

implicit function is an inverse function. Not all functions have a unique inverse function. If g is a function of x that has a unique inverse, then the...

→ X admits an inverse function f −1, negative functional powers f −n are defined for n > 0 as the negated power of the inverse function: f −n = (f −1)n...

notion is rarely used. Image and inverse image may also be defined for general binary relations, not just functions. The word "image" is used in three...

function, and then convert it to the equivalent inverse function using the relationship between the two given above. In this way the inverse function...

the implicit function theorem. Inverse function theorem Constant rank theorem: Both the implicit function theorem and the inverse function theorem can...

\end{aligned}}} The inverse of Φ is known as the normal quantile function, or probit function and may be expressed in terms of the inverse error function as probit...

More generally, a function has a left inverse for function composition if and only if it is injective, and it has a right inverse if and only if it is...

exponential function is the inverse function of the natural logarithm. The inverse function theorem implies that the natural logarithm has an inverse function, that...

integers to the even numbers, which has the division by two as its inverse function. A function is bijective if and only if it is both injective (or one-to-one)—meaning...

An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating...

interval I, it has an inverse function, which is a real function with domain f(I) and image I. This is how inverse trigonometric functions are defined in terms...

roots, logarithms, and inverse trigonometric functions. To define a single-valued function from a complex multivalued function, one may distinguish one...

behavior of f. In particular, the function f has a differentiable inverse function in a neighborhood of a point x if and only if the Jacobian determinant...

Additive inverse (negation), the inverse of a number that, when added to the original number, yields zero Compositional inverse, a function that "reverses"...

In mathematics, the logarithm to base b is the inverse function of exponentiation with base b. That means that the logarithm of a number x to the base b...

trigonometric functions has a corresponding inverse function, and an analog among the hyperbolic functions. The oldest definitions of trigonometric functions, related...

therefore are not one-to-one). A function may be strictly monotonic over a limited a range of values and thus have an inverse on that range even though it...