# Function composition

In mathematics, function composition is an operation  ∘  that takes two functions f and g, and produces a function h = g  ∘  f such that h(x) = g(f ). In this operation, the function g is applied to the result of applying the function f to x. That is, the functions f : X → Y and g : Y → Z are composed to yield a function that maps x in domain X to g(f ) in codomain Z. Intuitively, if z is a function of y, and y is a function of x, then z is a function of x. The resulting composite function is denoted g ∘ f : X → Z, defined by (g ∘ f )(x) = g(f ) for all x in X.
Inverse function
In mathematics, the inverse function of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by
Kuroda normal form
In formal language theory, a context-sensitive grammar is in Kuroda normal form if all production rules are of the form:AB → CD or A → BC or A → B or A
Free lattice
In mathematics, in the area of order theory, a free lattice is the free object corresponding to a lattice. As free objects, they have the universal property
Dependency relation
In computer science, in particular in concurrency theory, a dependency relation is a binary relation on a finite domain , symmetric, and reflexive; i.e. a finite tolerance relation. That is, it is a finite set of ordered pairs , such thatIf then
Image (mathematics)
In mathematics, the image of a function is the set of all output values it may produce
String operations
In computer science, in the area of formal language theory, frequent use is made of a variety of string functions; however, the notation used is different from that used for computer programming, and some commonly used functions in the theoretical realm
Blake canonical form
In Boolean logic, a formula for a Boolean function f is in Blake canonical form (BCF), also called the complete sum of prime implicants, the complete sum, or the disjunctive prime form, when it is a disjunction of all the prime implicants of f
Iterated function
In mathematics, an iterated function is a function X → X which is obtained by composing another function f : X → X with itself a certain number of times. The process of repeatedly applying the same function is called iteration. In this process
Semiautomaton
In mathematics and theoretical computer science, a semiautomaton is a deterministic finite automaton having inputs but no output. It consists of a set Q of states, a set Σ called the input alphabet, and a function T: Q × Σ → Q called the transition
Inzer (surname)
Inzer is a surname. People with that surname include:Drew Inzer, American football offensive lineman James C. Inzer (1887–1967), 16th Lieutenant Governor of Alabama William H. Inzer (1906–1978), Justice of the Supreme Court of