# Functions The notion of a function is that of something which provides a distinct output for a given input.

Definition

Think about two sets, D and R along with a principle which appropriates a unique element of R to each and every element of D. This rule is termed a function and it is represented by a letter such as f. Given n x ∈ D, f (x) is the name of the thing in R which comes from doing f to x. D is called the domain of f. In order to establish that D refers to f, the representation D (f) may be used. The set R is sometimes described as the range of f. Nowadays it.
is known as the codomain. The set of all elements of R which are of the form f (x) for some x ∈ D is consequently, a subset of R. This is sometimes referred to as the image of f. When this set equals R, the function f is said to be onto, also surjective, if whenever x  ̸= y it followss f (x) ̸= f (y), the function is called one-to-one, also injective.

It is typical representation to write f : D → R to denote the condition just described within this definition where f is a function characterized on a domain D which has values in a codomain R.