Answer to Question #147392 in Discrete Mathematics for imran khan

Question

Definition of Function, Domain, Codomain and Range, Well defined function, Types of functions(Injective ,Surjective, Bijective, Composite)

Answer 1

Definition of :

Function — is a relation between two sets that associates every element of the first set to exactly one element of the second set.

Domain — is the set of all possible inputs for the function.

Codomain — is the set of its possible outputs.

Range — is the set of the images of all elements from the domain.

Well defined (unambiguous) function — is a function, which gives the same result when the representation of the input is changed without changing the value of the input.

Types of functions:

Injective (one-to-one) function — is a function, where each element of the codomain is mapped to by at most one element of the domain.

Surjective (onto) function — is a function, where each element of the codomain is mapped to by at least one element of the domain.

Bijective (one to one and onto) funtion — is a function, where each element of the codomain is mapped to by exactly one element of the domain.

Composite function — is a function that takes two functions f(x) and g(x) and produces a function h(x), such that h(x) = g(f(x)).