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  2. Function composition - Wikipedia

    en.wikipedia.org/wiki/Function_composition

    During the mid-20th century, some mathematicians adopted postfix notation, writing xf for f(x) and (xf)g for g(f(x)). [17] This can be more natural than prefix notation in many cases, such as in linear algebra when x is a row vector and f and g denote matrices and the composition is by matrix multiplication. The order is important because ...

  3. Chain rule - Wikipedia

    en.wikipedia.org/wiki/Chain_rule

    In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g.More precisely, if = is the function such that () = (()) for every x, then the chain rule is, in Lagrange's notation, ′ = ′ (()) ′ (). or, equivalently, ′ = ′ = (′) ′.

  4. Function (mathematics) - Wikipedia

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

    In this notation, x is the argument or variable of the function. A specific element x of X is a value of the variable, ... For example, let f(x) = x 2 and g(x) ...

  5. Symmetric group - Wikipedia

    en.wikipedia.org/wiki/Symmetric_group

    The group operation in a symmetric group is function composition, denoted by the symbol ∘ or simply by just a composition of the permutations. The composition fg of permutations f and g, pronounced "f of g", maps any element x of X to f(g(x)). Concretely, let (see permutation for an explanation of notation):

  6. Mathematical notation - Wikipedia

    en.wikipedia.org/wiki/Mathematical_notation

    Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. For example, the physicist Albert Einstein's formula = is the quantitative representation in mathematical notation of mass–energy equivalence. [1]

  7. Iterated function - Wikipedia

    en.wikipedia.org/wiki/Iterated_function

    Because the notation f n may refer to both iteration (composition) of the function f or exponentiation of the function f (the latter is commonly used in trigonometry), 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 ...

  8. Codomain - Wikipedia

    en.wikipedia.org/wiki/Codomain

    A function f from X to Y. The blue oval Y is the codomain of f. The yellow oval inside Y is the image of f, and the red oval X is the domain of f. In mathematics, a codomain or set of destination of a function is a set into which all of the output of the function is constrained to fall. It is the set Y in the notation f: X → Y.

  9. Notation for differentiation - Wikipedia

    en.wikipedia.org/wiki/Notation_for_differentiation

    When f is a function of several variables, it is common to use "∂", a stylized cursive lower-case d, rather than "D". As above, the subscripts denote the derivatives that are being taken. For example, the second partial derivatives of a function f(x, y) are: [6]