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Inverse function

Index Inverse function

In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa. [1]

88 relations: Addison-Wesley, Addition, Axiom of choice, Bijection, Binary logarithm, Binary relation, Calculus, Category theory, Celsius, Cengage, Chain rule, Chapman & Hall, Codomain, Common logarithm, Constructivism (mathematics), Continuous function, Converse relation, CRC Press, Cube (algebra), Cube root, Cubic function, Derivative, Differentiable function, Division (mathematics), Domain of a function, Dover Publications, E (mathematical constant), Equation, Fahrenheit, Fiber (mathematics), Formula, Function (mathematics), Function composition, Function of several real variables, Henry Holt and Company, Horizontal line test, Hyperbolic function, Identity function, If and only if, Image (mathematics), Indecomposability, Injective function, Integer, Inverse function theorem, Inverse functions and differentiation, Inverse hyperbolic functions, Inverse trigonometric functions, Invertible matrix, Involution (mathematics), Iterated function, ..., Jacobian matrix and determinant, Lagrange inversion theorem, Leibniz's notation, Level set, Logarithm, Mathematics, Maxima and minima, Monotonic function, Morphism, Multiplication, Multiplicative inverse, Multivalued function, Natural logarithm, Ordered pair, Partial function, Pearson Education, Prentice Hall, Principal branch, Principal value, Range (mathematics), Real number, Reflection (mathematics), Reversible computing, Section (category theory), Set (mathematics), Set theory, Sine, Singleton (mathematics), Springer Science+Business Media, Square root, Subset, Subtraction, Surjective function, Thomson Corporation, Trigonometric functions, Uniqueness quantification, Universal quantification, W. H. Freeman and Company. Expand index (38 more) »

Addison-Wesley

Addison-Wesley is a publisher of textbooks and computer literature.

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Addition

Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.

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Axiom of choice

In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty.

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Bijection

In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

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Binary logarithm

In mathematics, the binary logarithm is the power to which the number must be raised to obtain the value.

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Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

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Calculus

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

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Category theory

Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).

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Celsius

The Celsius scale, previously known as the centigrade scale, is a temperature scale used by the International System of Units (SI).

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Cengage

Cengage is an educational content, technology, and services company for the higher education, K-12, professional, and library markets worldwide.

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Chain rule

In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions.

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Chapman & Hall

Chapman & Hall was a British publishing house in London, founded in the first half of the 19th century by Edward Chapman and William Hall.

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Codomain

In mathematics, the codomain or target set of a function is the set into which all of the output of the function is constrained to fall.

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Common logarithm

In mathematics, the common logarithm is the logarithm with base 10.

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Constructivism (mathematics)

In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists.

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Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

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Converse relation

In mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation.

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CRC Press

The CRC Press, LLC is a publishing group based in the United States that specializes in producing technical books.

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Cube (algebra)

In arithmetic and algebra, the cube of a number is its third power: the result of the number multiplied by itself twice: It is also the number multiplied by its square: This is also the volume formula for a geometric cube with sides of length, giving rise to the name.

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Cube root

In mathematics, a cube root of a number x is a number y such that y3.

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Cubic function

In algebra, a cubic function is a function of the form in which is nonzero.

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Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

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Differentiable function

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

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Division (mathematics)

Division is one of the four basic operations of arithmetic, the others being addition, subtraction, and multiplication.

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Domain of a function

In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.

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Dover Publications

Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.

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E (mathematical constant)

The number is a mathematical constant, approximately equal to 2.71828, which appears in many different settings throughout mathematics.

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Equation

In mathematics, an equation is a statement of an equality containing one or more variables.

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Fahrenheit

The Fahrenheit scale is a temperature scale based on one proposed in 1724 by Dutch-German-Polish physicist Daniel Gabriel Fahrenheit (1686–1736).

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Fiber (mathematics)

In mathematics, the term fiber (or fibre in British English) can have two meanings, depending on the context.

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Formula

In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Function composition

In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.

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Function of several real variables

In mathematical analysis, and applications in geometry, applied mathematics, engineering, natural sciences, and economics, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables.

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Henry Holt and Company

Henry Holt and Company is an American book publishing company based in New York City.

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Horizontal line test

In mathematics, the horizontal line test is a test used to determine whether a function is injective (i.e., one-to-one).

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Hyperbolic function

In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.

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Identity function

Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.

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If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

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Image (mathematics)

In mathematics, an image is the subset of a function's codomain which is the output of the function from a subset of its domain.

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Indecomposability

In constructive mathematics, indecomposability or indivisibility (Unzerlegbarkeit, from the adjective unzerlegbar) is the principle that the continuum cannot be partitioned into two nonempty pieces.

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Injective function

In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.

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Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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Inverse function theorem

In mathematics, specifically differential calculus, the inverse function theorem gives a sufficient condition for a function to be invertible in a neighborhood of a point in its domain: namely, that its derivative is continuous and non-zero at the point.

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Inverse functions and differentiation

In mathematics, the inverse of a function y.

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Inverse hyperbolic functions

In mathematics, the inverse hyperbolic functions are the inverse functions of the hyperbolic functions.

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Inverse trigonometric functions

In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains).

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Invertible matrix

In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.

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Involution (mathematics)

In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.

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Iterated function

In mathematics, an iterated function is a function (that is, a function from some set to itself) which is obtained by composing another function with itself a certain number of times.

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Jacobian matrix and determinant

In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.

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Lagrange inversion theorem

In mathematical analysis, the Lagrange inversion theorem, also known as the Lagrange–Bürmann formula, gives the Taylor series expansion of the inverse function of an analytic function.

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Leibniz's notation

dydx d2ydx2 In calculus, Leibniz's notation, named in honor of the 17th-century German philosopher and mathematician Gottfried Wilhelm Leibniz, uses the symbols and to represent infinitely small (or infinitesimal) increments of and, respectively, just as and represent finite increments of and, respectively.

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Level set

In mathematics, a level set of a real-valued function ''f'' of ''n'' real variables is a set of the form that is, a set where the function takes on a given constant value c. When the number of variables is two, a level set is generically a curve, called a level curve, contour line, or isoline.

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Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Maxima and minima

In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).

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Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

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Morphism

In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.

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Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

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Multiplicative inverse

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.

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Multivalued function

In mathematics, a multivalued function from a domain to a codomain is a heterogeneous relation.

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Natural logarithm

The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.

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Ordered pair

In mathematics, an ordered pair (a, b) is a pair of objects.

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Partial function

In mathematics, a partial function from X to Y (written as or) is a function, for some subset X ′ of X.

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Pearson Education

Pearson Education (see also Pearson PLC) is a British-owned education publishing and assessment service to schools and corporations, as well as directly to students.

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Prentice Hall

Prentice Hall is a major educational publisher owned by Pearson plc.

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Principal branch

In mathematics, a principal branch is a function which selects one branch ("slice") of a multi-valued function.

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Principal value

In complex analysis, the principal values of a multivalued function are the values along one chosen branch of that function, so that it is single-valued.

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Range (mathematics)

In mathematics, and more specifically in naive set theory, the range of a function refers to either the codomain or the image of the function, depending upon usage.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Reflection (mathematics)

In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.

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Reversible computing

Reversible computing is a model of computing where the computational process to some extent is reversible, i.e., time-invertible.

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Section (category theory)

In category theory, a branch of mathematics, a section is a right inverse of some morphism.

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Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

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Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

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Sine

In mathematics, the sine is a trigonometric function of an angle.

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Singleton (mathematics)

In mathematics, a singleton, also known as a unit set, is a set with exactly one element.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Square root

In mathematics, a square root of a number a is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.

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Subset

In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

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Subtraction

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection.

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Surjective function

In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).

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Thomson Corporation

The Thomson Corporation was one of the world's largest information companies.

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Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

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Uniqueness quantification

In mathematics and logic, the phrase "there is one and only one" is used to indicate that exactly one object with a certain property exists.

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Universal quantification

In predicate logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all".

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W. H. Freeman and Company

W.

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Anti-function, Antifunction, Composition inverse, Compositional inverse, Function inverse, Functional inverse, General inverse function, Inv (function prefix), Inverse (function), Inverse (functions), Inverse functions, Inverse map, Inverse mapping, Inverse operation, Inverse operator, Inverse process, Invertible function, Left inverse function, Partial inverse, The Inverse Operation.

References

[1] https://en.wikipedia.org/wiki/Inverse_function

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