Section Objectives
Besides transforming individual functions, two or more functions can be combined in lots of ways to produce new functions.
The most basic combinations of functions come from the four basic arithmetic operations.
Given the following table of values, compute , , and . (Solution)
x | f(x) | g(x) |
---|---|---|
0 | 5 | 2 |
1 | -3 | 7 |
2 | 10 | -2 |
3 | -8 | -10 |
Another useful and important way of combining functions is to form the composition. Functions are composed when the output of one function is used as the input for a second function.
The composition of and , written , is the new function . In a composition of functions, the output of the first function is the input of the second.
For further help...