Compound function is a common mathematical concept, which refers to a function composed of two or more basic functions. In the compound function, both the inner function and the outer function can be simple elementary functions, such as linear function, quadratic function and proportional function.

The synthesis process of composite function is very simple, just combine two or more basic functions in a certain order. For example, if we have an external function f(x) and an internal function g(x), then the composite function f(g(x)) can be expressed as f(g(x)) = f(g(x)).

The decomposition of composite function is complicated, and some methods in mathematical analysis are needed. Generally speaking, we can regard the composite function as a "black box" and understand its properties by observing the input and output. Specifically, we can substitute the input value of the composite function into the inner function to get the output value of the inner function, and then substitute this output value into the outer function to get the final output value. In this way, we can decompose the composite function into internal function and external function.

In practical application, the concepts of composite function and decomposition are very useful. For example, in machine learning, we can use composite functions to represent a complex model and map input data to output results; In circuit analysis, we can use decomposition method to decompose a complex circuit system into several basic circuit components, thus simplifying the analysis process.

In a word, composite function is a very important mathematical concept, which can represent many complex functional relationships. By mastering the composition and decomposition process of composite functions, we can better understand and analyze these functional relationships.