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  2. Function composition - Wikipedia

    en.wikipedia.org/wiki/Function_composition

    Thus, the function g is applied after applying f to x. Reverse composition, sometimes denoted , applies the operation in the opposite order, applying first and second. Intuitively, reverse composition is a chaining process in which the output of function f feeds the input of function g.

  3. Inverse function - Wikipedia

    en.wikipedia.org/wiki/Inverse_function

    The function g must equal the inverse of f on the image of f, but may take any values for elements of Y not in the image. A function f with nonempty domain is injective if and only if it has a left inverse. [21] An elementary proof runs as follows: If g is the left inverse of f, and f(x) = f(y), then g(f(x)) = g(f(y)) = x = y.

  4. Concatenation - Wikipedia

    en.wikipedia.org/wiki/Concatenation

    v. t. e. In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end. For example, the concatenation of "snow" and "ball" is "snowball". In certain formalisations of concatenation theory, also called string theory, string concatenation is a primitive notion.

  5. Microsoft Excel - Wikipedia

    en.wikipedia.org/wiki/Microsoft_Excel

    Microsoft Excel A simple bar graph being created in Excel, running on Windows 11 Developer(s) Microsoft Initial release November 19, 1987 ; 36 years ago (1987-11-19) Stable release 2312 (Build 17126.20132) / January 9, 2024 ; 9 months ago (2024-01-09) Written in C++ (back-end) Operating system Microsoft Windows Type Spreadsheet License Trialware Website microsoft.com microsoft-365 /excel ...

  6. Computation of cyclic redundancy checks - Wikipedia

    en.wikipedia.org/wiki/Computation_of_cyclic...

    Computation of a cyclic redundancy checkis derived from the mathematics of polynomial division, modulo two. In practice, it resembles long divisionof the binarymessage string, with a fixed number of zeroes appended, by the "generator polynomial" string except that exclusive oroperations replace subtractions.

  7. Inverse hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_hyperbolic_functions

    They are commonly denoted by the symbols for the hyperbolic functions, prefixed with arc-or ar-. For a given value of a hyperbolic function, the inverse hyperbolic function provides the corresponding hyperbolic angle measure, for example arsinh⁡(sinh⁡a)=a{\displaystyle \operatorname {arsinh} (\sinh a)=a}and sinh⁡(arsinh⁡x)=x ...

  8. Pointwise - Wikipedia

    en.wikipedia.org/wiki/Pointwise

    Pointwise. In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value of some function An important class of pointwise concepts are the pointwise operations, that is, operations defined on functions by applying the operations to function values separately for each point in the domain ...

  9. Inverse Laplace transform - Wikipedia

    en.wikipedia.org/wiki/Inverse_Laplace_transform

    Post's inversion formula for Laplace transforms, named after Emil Post, [3] is a simple-looking but usually impractical formula for evaluating an inverse Laplace transform. The statement of the formula is as follows: Let f ( t ) {\displaystyle f(t)} be a continuous function on the interval [ 0 , ∞ ) {\displaystyle [0,\infty )} of exponential ...

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