1.5 Combinations of Functions
Objective: You will be able to:
find arithmetic combinations and compositions of functions
Jul 21­10:47 PM
Warm Ups...
State the domain of the functions:
1. y = 2x2 + 5
x2 ­ 4
2. y = ­3x + 7
3. f(x) = √(3x + 6)
Aug 29­2:27 PM
1
You will be able to find arithmetic combinations and compositions of functions
Given: f(x) = 2x + 1 and g(x) = x2 +2x ­ 1
a. Find (f ­ g)(x)
b. State the domain
c. Find (f ­ g)(2)
Jul 21­10:49 PM
You will be able to find arithmetic combinations and compositions of functions
Given: f(x) = √x and g(x) = √(4 ­ x2)
a. Find (f/g)(x) and (g/f)(x)
b. State the domain of each
Jul 21­10:53 PM
2
You will be able to find arithmetic combinations and compositions of functions
Compositions of Functions
f(g(x)) = (f g)(x) = "f of g of x"
Jul 21­10:55 PM
You will be able to find arithmetic combinations and compositions of functions
Given: f(x) = √x, and g(x) = x ­ 1
a. Find f g, and state the domain.
b. Find g f, and state the domain.
c. Find (f g)(2) and (f g)(0)
Jul 29­2:24 PM
3
You will be able to find arithmetic combinations and compositions of functions
Given: f(x) = 2x + 3, and g(x) = 1/2(x ­ 3)
a. Find f g, and state the domain.
b. Find g f, and state the domain.
Jul 29­2:31 PM
You will be able to find arithmetic combinations and compositions of functions
Write the function h(x) = (3x ­ 5)3 as a composition of two functions.
Jul 29­2:36 PM
4
You will be able to find arithmetic combinations and compositions of functions
Write the function h(x) = 1 as a composition of two functions.
(x ­ 2)2
Jul 29­2:36 PM
You will be able to find arithmetic combinations and compositions of functions
Use the graphs of f and g to graph:
a. g(x) + 4
b. f(x ­ 4) c. h(x) = (f + g)(x)
f
g
Jul 29­2:40 PM
5
Aug 31­3:02 PM
6