Module 7: Rational Functions and Function Operations

 

Explore

 

Multiplying and dividing functions is a straightforward process that is similar to adding or subtracting functions. In Try This 1 you found p(x) = (fg)(x) and Your calculations and domain explanations may have been similar to what is shown.

 

 

 

 

 

 

 

Domain →
Use the x-values where both f(x) and g(x) are defined.

 

 

where g(x) ≠ 0 and so x ≠ 3

 

Domain →
g(x) ≠ 0; use the x-values where both f(x) and g(x) are defined, less any value that makes g(x) = 0.

 

Determining the range of p(x) = (fg)(x) or g(x) ≠ 0 can be more difficult. This can often be interpreted from the graph of the function.



textbook

To see another example of how functions can be multiplied, review “Example 1” on pages 490 and 491 of the textbook. To review an example of dividing functions, read “Example 2” on pages 491 to 493. Note how non-permissible values are identified once the f(x) and g(x) functions have been substituted into h(x).

 

Self-Check 1

 

Complete questions 1.a., 1.c., 6.b., 6.c., 7.b., 7.c., 8.b., and 8.c. on page 496 of the textbook. Answer