Abstract function is an abstract mathematical concept, which describes the same characteristics of a class of functions, while composite function is a function that combines two or more functions to operate. Specifically, an abstract function is a function expression, in which parameters and return values are abstract concepts, and a composite function is a function that combines two or more functions to operate.

In compound functions, each function has its own parameters and return values, which are combined to form a new function. Therefore, the composite function can be regarded as a more complex abstract function, which combines multiple functions to achieve more complex functions.

Compound function:

Not any two functions can be combined into a composite function, only when Mx∩Du≦? The two can form a composite function. Let the domain of function y=f(x) be Du and the domain of function u=g(x) be Mu, 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, a functional relationship is formed between the variables X and Y by the variable U, and this function is called a composite function, which is recorded as: y=f[u(x)], where X is called an independent variable, U is an intermediate variable, and Y is a dependent variable (that is, a function).

Abstract function:

Abstract function is a mathematical term. Because this kind of questions can comprehensively examine students' understanding of the concept and nature of functions, at the same time, abstract function questions set the definition range, range, monotonicity, parity, periodicity and visualization of functions in one.

Therefore, it constantly appears in the college entrance examination; For example, the 2002 Shanghai College Entrance Examination 12 questions, the 2004 Jiangsu College Entrance Examination 22 questions, and the 2004 Zhejiang College Entrance Examination 12 questions.

Not any two functions can be combined into a composite function, only when Mx∩Du≦? The two can form a composite function. Therefore, not every function can write the original function.