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  2. Function (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Function_(mathematics)

    For example, let f(x) = x 2 and g(x) = x + 1, then (()) = + and (()) = (+) agree just for = The function composition is associative in the sense that, if one of ( h ∘ g ) ∘ f {\displaystyle (h\circ g)\circ f} and h ∘ ( g ∘ f ) {\displaystyle h\circ (g\circ f)} is defined, then the other is also defined, and they are equal, that is, ( h ...

  3. List of mathematical functions - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_functions

    Indicator function: maps x to either 1 or 0, depending on whether or not x belongs to some subset. Step function: A finite linear combination of indicator functions of half-open intervals. Heaviside step function: 0 for negative arguments and 1 for positive arguments. The integral of the Dirac delta function. Sawtooth wave; Square wave ...

  4. List of types of functions - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_functions

    Composite function: is formed by the composition of two functions f and g, by mapping x to f (g(x)). Inverse function : is declared by "doing the reverse" of a given function (e.g. arcsine is the inverse of sine ).

  5. Elementary function - Wikipedia

    en.wikipedia.org/wiki/Elementary_function

    A differential field F is a field F 0 (rational functions over the rationals Q for example) together with a derivation map u → ∂u. (Here ∂u is a new function. Sometimes the notation u′ is used.) The derivation captures the properties of differentiation, so that for any two elements of the base field, the derivation is linear

  6. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    For example, if is a function of and ⁠ ⁠, then its partial derivatives measure the variation in in the and direction. However, they do not directly measure the variation of f {\displaystyle f} in any other direction, such as along the diagonal line ⁠ y = x {\displaystyle y=x} ⁠ .

  7. Graph of a function - Wikipedia

    en.wikipedia.org/wiki/Graph_of_a_function

    Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.

  8. Domain of a function - Wikipedia

    en.wikipedia.org/wiki/Domain_of_a_function

    A function f from X to Y. The set of points in the red oval X is the domain of f. Graph of the real-valued square root function, f(x) = √ x, whose domain consists of all nonnegative real numbers. In mathematics, the domain of a function is the set of inputs accepted by the function.

  9. Function composition - Wikipedia

    en.wikipedia.org/wiki/Function_composition

    To avoid ambiguity, some mathematicians [citation needed] choose to use ∘ to denote the compositional meaning, writing f ∘n (x) for the n-th iterate of the function f(x), as in, for example, f ∘3 (x) meaning f(f(f(x))). For the same purpose, f [n] (x) was used by Benjamin Peirce [14] [11] whereas Alfred Pringsheim and Jules Molk suggested ...