A27­6CompositionOfFunctionsNotes.notebook
August 25, 2015
Operations with Functions
Algebra 2
Ch.7 Notes Page 5
f(x) = 3x + 8
g(x) = 2x ­ 12
Domains are the x­values that are the domains of both functions.
P5 7­6 Function Operations
Addition (f + g)(x) = f(x) + g(x)
Subtraction (f ­ g)(x) = f(x) ­ g(x)
Aug 19­6:20 AM
Nov 8­8:59 AM
Operations with Functions
Domains are the x­values f(x) = x ­ 1
that are the domains of g(x) = x + 1
both functions.
Multiplication (f x g)(x) = f(x) x g(x)
2
Composite Functions
The output of the first function becomes the input for the second function.
1. Evaluate the inner function f(x) first
2. Use the Result as the input of the outer function g(x)
Read as G of F of X
Division (f/g)(x) = f(x)/g(x) g(x) ≠0
f(x) = x ­ 2
g(x) = x2 Find g(f(­5))
Nov 13­7:01 AM
Find f(g(­5))
Nov 13­7:09 AM
Example: Discount and % off
HW #5
Please put your name and class period at the top of
the homework. Also include the homework number.
7­6 WS (Add #1­8 on Back)
f(x) = 3x + 5 g(x) = x2
1. f(x) + g(x)
2. g(x) ­ f(x)
3. f(x) x g(x)
4. f(x) / g(x)
5. f(g(2))
6. g(f(2))
7. f(g(c))
8. g(f(c))
You have a Coupon for $5 off any item in a store.
The store is also having a 20% off sale.
Cost with 20% off
f(x) = x ­ .2x = .8x
Find g(f(x)) = 20% off first
Cost with Coupon for $5 off
g(x) = x ­ 5
Find f(g(x)) = $5 off first
How much more is any item if the Coupon is applied first?
Aug 19­6:25 AM
Nov 13­7:28 AM
1
A27­6CompositionOfFunctionsNotes.notebook
Extra Practice...
10% discount on all items. In addition, employees get a 25% discount.
August 25, 2015
You are shopping at a store and all items are 20% off. You also got a coupon for an additional $5 off.
Option A:
Option B:
Use the 20% off first and Use the $5 off first and
then the $5 after the discount.
then the 20% after that.
Which would you choose? Does it matter?
Jan 7­7:55 AM
Jan 7­7:55 AM
Do you agree?
f(x) = 0.8x and g(x) = x ­ 5
Apply Discount First
Apply Coupon First
Jan 7­7:55 AM
2