Jabarkan Dadaran formal dari Fungsi (matematika) dalam bahasa sunda

Formally, a function f from a set X of input values to a set Y of possible output values (written as f : X → Y) is a relation between X and Y which satisfies:

f is total: for all x in X, there exists a y in Y such that x f y (x is f-related to y), i.e. for éach input value, there is at léast one output value in Y.

f is many-to-one: if x f y and x f z, then y = z. i.e., many input values can be related to one output value, but one input value cannot be related to many output values.

For éach input value x in the domain, the corresponding unique output value y in the codomain is denoted by f(x).

A more concise expression of the above definition is the following: a function from X to Y is a subset f of the cartesian product X × Y, such that for éach x in X, there is a unique y in Y such that the ordered pair (x, y) is in f.

The set of all functions f : X → Y is denoted by YX. Note that |YX| = |Y||X| (refer to Cardinal numbers).

A relation between X and Y that satisfies condition (1) is a multivalued function. Every function is a multivalued function, but not every multivalued function is a function. A relation between X and Y that satisfies condition (2) is a partial function. Every function is a partial function, but not every partial function is a function. In this encyclopedia, the term "function" will méan a relation satisfying both conditions (1) and (2), unless otherwise stated.

Consider the following three examples: