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# Usefulness of composite functions

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Composite functions are useful when one quantity depends on a second quantity, and in turn that second quantity depends on a third quantity. This is an extremely general situation with lots of real-world applications.

1. The cost of getting new life insurance depends on how old you are, and how old you are depends on what year you were born. Provide an example a composite function using these variables.

2. The amount of time it takes to get to work depends on how much traffic there is, and the amount of traffic there is depends on what time of day it is. If we call the amount of traffic C and the time of day t, then C is a function of t. If we call the time it takes to get to work W, then W is a function of C. Provide an example of a composite function using these variables.

3. Make up your own example of a composite function. Be sure to explain (1) what your variables are, (2) how they are represented in the function, and (3) which elementary functions are combined to form the composite function.

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Answer

1. Suppost A(t) is the function of your age, so A(t)=2013-t where 2013 is the current year and t is your birth year. Since life insurance depends on your age and let C be a function of life ...

#### Solution Summary

The usefulness of composite functions are determined. Extremely general situations with lots of real-world applications are provided.

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