1. Combinations of Functions: Composite Functions
1.8

2. Sum, Difference, Product, and Quotient
(f+g)(x) = f(x) + g(x)
(f-g)(x) = f(x) – g(x)
(fg)(x) = f(x) * g(x)
(f/g)(x) = f(x)/g(x), g(x)≠0
Sum, Difference, Product, and Quotient

3. The domain of these functions is the intersection of the domains of f(x) and g(x).
Keep is mind with division, the denominator can not = 0
Domain

4. Find the sum and difference of f and g. State the domain
𝑓 𝑥 =2𝑥+1, 𝑔 𝑥 = 𝑥 2 +2𝑥−1
𝑓+𝑔 𝑥 =
𝑔−𝑓 𝑥 =
Find the sum and difference of f and g. State the domain

5. Find the product and state the domain
𝑓 𝑥 = 𝑥 𝑔 𝑥 =𝑥−3
𝑓𝑔 𝑥 =
Find the product and state the domain

6. Find the Quotient and state the domain
𝑓 𝑥 = 𝑥 𝑔 𝑥 = 4− 𝑥 2
𝑓 𝑔 𝑥 =
𝑔 𝑓 𝑥 =
Find the Quotient and state the domain

7. Composition of Functions
Using one function as the argument for another function.
𝑓°𝑔 𝑥 =𝑓(𝑔 𝑥 )
Domain: all values in the domain of g such that g(x) is in the domain of f
****remember to keep g(x) in mind
Composition of Functions

8. Evaluate and state the domain
𝑓 𝑥 = 𝑥 2 − 𝑔 𝑥 = 9− 𝑥 2
𝑓°𝑔 𝑥 =
Evaluate and state the domain

9. Decomposing Functions
Write ℎ 𝑥 = 1 (𝑥−2 ) 2 as the composition of two functions
Decomposing Functions

10. p. 81: 3, 4, 5-25 odd, odd.
Homework