1. Determine the form of the composite function: First, we need to know the specific form of the composite function, such as f(g(x)) or g(f(x)). This will help us understand how to decompose it into simpler functions.
2. Determine the internal function and external function: In a composite function, there is usually an internal function and an external function. An internal function is a function nested in another function, while an external function is a function containing an internal function. For example, in f(g(x)), g(x) is an inner function and f(x) is an outer function.
3. Replace the internal function with the inverse function (if it exists): If the internal function has the inverse function, we can replace it with X .. This will enable us to convert the composite function into a simple external function. For example, if g(x) is an inner-layer function and it has an inverse function g (- 1) (x), the composite function f(g(x)) can be replaced by f (g (- 1) (x).
4. Simplify the external function: Now, we have converted the composite function into a simple external function. Next, we need to simplify this external function. This may include the use of algebraic techniques (such as distribution law, correlation law, etc.). ) or in a simpler form (such as polynomial, exponent, etc.). ).
5. Repeat the above steps: If the composite function is still complex, we can repeat the above steps until we find a simple enough expression to represent the composite function.
6. Check results: Finally, we need to check whether our decomposition is correct. This can be achieved by comparing the original composite function with our decomposition results. If our decomposition result is equal to the original composite function, then we can be sure that our decomposition is correct.
In a word, the decomposition of composite function needs to identify the internal and external functions, and then simplify the external functions with algebraic skills. By repeating these steps, we can decompose complex compound functions into simpler and more understandable functions.