Given a number set A, assuming that the element in it is X, now apply the corresponding rule F to the element X in A, and record it as f(x), and get another number set B. Assuming that the element in B is Y, the equivalent relationship between Y and X can be expressed as y=f(x).

For example, y=x, or f(x)=x means the same thing.

F(a)=0 means that in this function f(x), when x=a, the function value is 0.

Origin of function

The word "function" used in China's math book is translated. It was Li, an algebra expert in Qing Dynasty, who translated "function" into "function" when he translated Algebra (1859).

In ancient China, the word "Xin" and the word "Han" were universal and both had the meaning of "Han". Li's definition is: "every formula contains heaven, which is a function of heaven." In ancient China, four different unknowns or variables were represented by four words: heaven, earth, people and things. The meaning of this definition is: "Whenever a formula contains the variable X, the formula is called a function of X."

So "function" means that the formula contains variables. The exact definition of the equation we are talking about refers to the equation with unknowns. However, in the early mathematical monograph "Nine Chapters Arithmetic" in China, the word "equation" means simultaneous linear equations with many unknowns, that is, the so-called linear equations.