Describe the relationship of input and output values for composite functions.
The relationship of input and output values for composite functions can be defined as follows:
1. The input value of the composite function is first applied to the inner function.
2. The output of the inner function becomes the input for the outer function.
3. The final output of the composite function is the result of applying the outer function to the output of the inner function.
In other words, when evaluating a composite function, the input value is "processed" by both the inner and outer functions consecutively. The output value explicitly depends on the actions performed by both functions.
To illustrate this relationship with an example, let's consider the composite function f(g(x)), where g(x) and f(x) are two separate functions:
1. We start by applying an input value, let's say x, to the inner function g(x). The output of g(x) is then obtained.
2. This output becomes the input for the outer function f(x). f(g(x)) is evaluated using the output from step 1.
3. The final output of the composite function f(g(x)) is the result obtained from step 2.
It is important to note that the input and output values of the composite function depend on the specific functions involved and the values being used. The relationship can vary depending on the nature of the functions and their respective actions on the input values.