Complex Numbers Add and Subtract complex numbers Multiply and divide complex numbers.
1.5 Combintions of Functions Students will be able to: - add, subtract, multiply, and divide...
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Transcript of 1.5 Combintions of Functions Students will be able to: - add, subtract, multiply, and divide...
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.