Generally speaking, in a changing process, it is assumed that there are two variables X and Y. If there is a unique Y corresponding to any X, then X is called an independent variable, and Y is a function of X. The range of X is called the domain of the function, and the range of Y is called the domain of the function.

Modern definition

Let a and b be non-empty number sets. If any number x in set A has a unique number in set B according to some corresponding relation F ..

Corresponding to it, then it is called mapping.

Is a function from set a to set b, written as

or

Where x is called an independent variable,

A function is called x, a set is called the domain of the function, and y corresponding to x is called the function value.

The set of function values is called the range of functions.

Among them, the domain of definition, the domain of value and the corresponding laws are called the three elements of a function.

Generally written as

If the domain is omitted, it is usually a set of meaningful directional functions.