Functions can be added, subtracted, multiplied and divided creating new functions and graphs that are complicated combinations of the various original functions. One important way to transform functions is through function composition. Function composition allows you to line up two or more functions that act on an input in tandem.
Is function composition essentially the same as multiplying the two functions together?
Composition of Functions
A common way to describe functions is a mapping from the domain space to the range space:
Function composition means that you have two or more functions and the range of the first function becomes the domain of the second function.
Earlier, you were asked if function composition is the same as multiplying two functions together. Function composition is not the same as multiplying two functions together. With function composition there is an outside function and an inside function. Suppose the two functions were doubling and squaring. It is clear just by looking at the example input of the number 5 that 50 (squaring then doubling) is different from 100 (doubling then squaring). Both 50 and 100 are examples of function composition, while 250 (five doubled multiplied by five squared) is an example of the product of two separate functions happening simultaneously.
For the next two examples, use the functions below:
For the next two examples, use the graphs shown below:
To see the Review answers, open this PDF file and look for section 1.11.