The meaning of this definition is: "Whenever a formula contains a variable X, the formula is called a function of X", so "function" means that the formula contains a variable. 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 term equation refers to simultaneous linear equations with many unknowns, that is, the so-called linear equations.
Let the domain of function y=f(x) be Du, and the domain of function u=g(x) be Dx and Mx. If Mx∩Du≦, then any X in Mx∩Du passes through U; If there is a uniquely determined value of y corresponding to it, the functional relationship between the variables X and Y is formed by the variable U, which is called a composite function, and is recorded as: y=f[g(x)], where X is called an independent variable, U is an intermediate variable, and Y is a dependent variable (i.e. a function).
The conditions for judging whether two functions can form a coincidence function are as follows:
Not any two functions can be combined into a composite function. Only when the intersection of the range Zφ of μ=φ(x) and the domain Df of y=f(μ) is not an empty set can they be combined into a composite function.