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Section 2.6
Combinations of Functions:
Composite Functions

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

Combination Functions in Real Life

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

1

Section 2.6 Objectives
• Find the domain of a function.
• Combine functions using the algebra of functions, specifying domains.
• Form composite functions.

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

The Domain of a Function

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

2

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

Steps to Determining Domain

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

3

Domains of Other Functions

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

Example

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

4

Example

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

The Algebra of Functions

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

5

NOTE: You must determine the domain before you simplify.

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

6

Determining Domains When Adding or
Subtracting Functions

Continued on next slide

Adapted
R.
Continuation of the same from Blitzer, New(2010). College Algebra Essentials problem. Pearson Education.
(Third Edition).
Jersey:

7

Determining Domains when Multiplying Functions

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

Example

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

8

Example

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

Example

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

9

Example

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

Composite Functions

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

10

The domain of the composite function is the intersection of the domain of g(x) with the domain of f(g(x)).

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

11

Example

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

Example

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

12

Decomposing Functions

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

13

Example

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

Example

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

14

(a)
(b)
(c)
(d)

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

(a)
(b)
(c)
(d)

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

15

(a)
(b)
(c)
(d)

Adapted from Blitzer, R. (2010). College Algebra Essentials
(Third Edition). New Jersey: Pearson Education.

16…...

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