Chapter 3.6 Operations of Functions

Pindling College Algebra   by Example  Series

Key Concept. Understand the basic arithmatic operations of functions.

Skills to Learn:

1. Know how to perform simple arithmatic operations on functions

2. Know how to derive composite functions

3. Know how to determine the domain of compsoite functions

Definitions of Arithmatic Operations of Functions

Given any two functions , they can be combined in these fashion: Example: Added: Example: Subtracted: Example: Multiplied: Example: Divided: Example: Domains: for arithmatic operations of is values of x where both the domain of are the same (interections of both domains)

Arithmatic Operations

Find and their domains (assume domain is all values of x unless otherwise stated)

Example 1. For , Domain

Example 2. For , Domain all values of x (for emphasis)

Example 3. For Domain Domain

Example 4. For Domain Domain Domain

Example 5. For Domain or (-2, 4) Domain Domain Domain , note x cannot be 4

Example 6. For Domain Domain Domain Domain , note x cannot be 0

Composite Functions ( )

Composite Function Domain is all values in domain of g(x) for which g9x0 is in the domain of f(x) Identity Function

Example 7. Find if Find Domain of g(x) is all values of x Find Domain of g(x) is all values of x Find Domain of g(x) is all values of x Find Domain of g(x) is all values of x

Example 8. Find if Find Domain for and domain for So Domain of is Find Domain for and domain for So Domain of is

Example 9. Find if Find Domain of g(x) is all values of x So Domain of is Find Domain of f(x) is and Domain of

Example 10. Find if Find Domain for and domain for So Domain of is Find Domain for and domain for is all So Domain of is