What is the definition of a function? Urgent. . . .

Traditional definition of function: suppose there are two variables x and y in a certain change process. If y has a unique fixed value corresponding to each fixed value of x within a certain range, then y is called a function of x and x is called an independent variable. We call the set of values of independent variable X as the domain of function, the value of Y corresponding to independent variable X as the value of function, and the set of function values as the domain of function. Modern definition of function: Let A and B be sets of non-empty numbers, and F: X → Y be corresponding rules from A to B, then the mapping F: A → B from A to B is called a function, and it is denoted as y=f(x), where x∈A, y∈B and the original image set A are called the definition of function F (x). The symbol y=f(x) is a mathematical expression of "Y is a function of X", which should be understood as: X is an independent variable and the object to which the law applies; F is the corresponding rule, which can be one or several analytic expressions, images, tables or text descriptions; Y is a function of the independent variable. When x is a specific allowable value, the corresponding y value is the function value corresponding to the independent variable value. When f is expressed by an analytical formula, the analytical formula is the resolution function. Y=f(x) is just a function symbol, which does not mean "Y equals the product of f and x", and f(x) is not necessarily an analytical formula. In the study of functions, besides the symbol f(x), symbols such as g(x), F (x) and G(x) are often used.