In high school, we learned the concept of composite functions . The concepts of composite functions learned in college are basically the same as those learned in high school. In application, more attention needs to be paid to composite issues related to piecewise functions .

　　1. Definition of composite function

　　Suppose the domain of function is and the range of function is , if

,

Then the function is called a composite function of . Among them, is called the independent variable, is called the dependent variable, and is called the intermediate variable.

　　Note: Not any two functions can be composed into a composite function.

　　For example, given the function

, ,

Since the domain of the former is and the latter is , these two functions cannot be combined into a composite function.

　　2. Find the expression of composite function

　　First, the domain of the composite function should be found, and the analysis should be carried out based on the interval segment of the domain of the outermost function, combined with the expression of the intermediate variable and the domain of the intermediate variable.

　　(1) Suppose the domain of function is , then the domain of composite function can be solved by the inequality ;

　　(2) Suppose the domain of function is , then the domain of function is the value domain of function when .

　　Then, write the expression of the composite function according to the definition .

　　3. The decomposition principle of composite functions from outside to inside , layer by layer .