1. Functions Operations. What you’ll learn
To add, subtract, multiply, and divide functions.
To find the composite of two functions.

2. Take a note: The domains of the sum, difference, product, and
quotient functions consists of the
x-values that are in the domains of both
f and g. Also, the domain of the
quotient function does not contain any
x-value for which g(x) ≠0.

3. Answers Your turn: Answers What are their domains? Example #1
The domain of f is the set of all real numbers.
The domain of g is all x≥0.
The domain of both f+g and f-g is the set of numbers common to the domains of both f and g, which is all x≥0.
Your turn:
Answers

4. Answer Answers Example #2: Multiplying and Dividing Functions.
The domain of both f and g is the set of all real numbers, so
the domain of is also the set of all real numbers.
The domain of is the set of all real numbers except x≠3.
Even though, after simplification is all real numbers.
Your turn:
Answers

5. Then use f(x) as the input for g.
Take a note:
Evaluate f(x) first.
Then use f(x) as the input for g.
Example #3: Composing Functions.
Answer
Your turn
Answer 4

6. Answer Cost using the coupon: C(x)=c-5
Example 4: Using Composite Functions.
You have a coupon good for $5 off the price of any large pizza.
You also get a 10% discount on any pizza if you show your
student ID. How much more would you pay for a large pizza if
the cashier applies the coupon first?
Answer
Let x=the price of a large pizza.
Cost using the coupon: C(x)=c-5
Cost using the 10% discount:
Compose the functions to apply
the discount then the coupon
Compose the functions to apply
the coupon and then the discount.
Subtract the functions:
You pay $.50 more if
the cashier applies
the coupon first.

7. Answer D(x)=cost after applying 15% store discount.
Your turn: A store is offering a 15% discount on all items. Also,
employees get a 20% employee discount. Write composite
functions.
To model taking the 15% discount and then 20% discount.
To model taking 20% discount and then 15% discount.
If you were an employee, which discount would you take first and why?
Answer
D(x)=cost after applying 15% store discount.
E(x)= cost after applying the 20% employee discount,
and x=cost of items.

8. CW odd and HW even