1.5 Combintions of FunctionsStudents will be able to:

- add, subtract, multiply, and divide functions.

- find compositions of one function with another.

- Use combinations of two functions to model and solve real-life problems.

Sum, Difference, Product, and Quotient of Function

Sum: (f+g)(x) = f(x) + g(x)

Difference: (f-g)(x) = f(x) – g(x)

Product: (fg)(x) = f(x)•g(x)

Quotient: f

gx

f x

g xg x

( ), ( ) 0

Example 1:

Given and , find . Then evaluate the sum when x = 2.

f x x( ) 2 1 g x x x( ) 2 2 1 ( )( )f g x

Example 2:

Given and , find (f – g)(x). Then evaluate the difference when x = 2.

f x x( ) 2 1 g x x x( ) 2 2 1

Example 3

Given and , find (fg)(x). Then evaluate the product when x = 4.

f x x( ) 2 g x x( ) 3

Example 4:

Find (f/g)(x) and (g/f)(x) for the functions given byand . Then find the domains of

each.

f x x( )

g x x( ) 4 2

Example 5:

Find for , . If possible, find and .

( )( )f g x f x x( ) x 0( )( )f g 2 ( )( )f g 0

Example 6:

Given f(x) = x + 2 and , evaluate (a)and (b) when x = 0,1,2, and 3.

g x x( ) 4 2 ( )( )f g x( )( )g f x

Example 7:

Find the domain of the composition for the functions given by and .f x x( ) 2 9 g x x( ) 9 2

( )( )f g x

Example 8:

Given and , find each composition.

a. b.

f x x( ) 2 3 g x x( ) ( ) 1

23

( )( )f g x ( )( )g f x

Example 9:

Write the function as a composition of two functions.h x x( ) ( ) 3 5 3

Example 10:

Write the function as a composition of two functions.h xx

( )( )

1

2 2

Composition of Functions:Convert miles to inches.

Example

X 0 1 2 3 4 5 6

F(x) 0 1.5 3 4.5 6 7.5 9

X 0 1.5 3 4.5 6 7.5 9

G(x) 0 5.25 10.5 15.75 21.0 26.25 31.5

F(x) displays the percent increase in UV radiation when the ozone layer thins by x%

G(x) displays the percent increases in cases of skin cancer given the % increase in UV radiation

G(F(2) =

Describe what G(F(x)) computes.