1. 1.8 Notes: Composite Functions
Date:
1.8 Notes: Composite Functions
Lesson Objective: Add, subtract, multiply and divide functions, find composite functions and use them in real-life apps.
Real-World App: What is the cost of producing x units of widgets with c cost?

2. Lesson 1: Performing Operations on Functions
Given f(x) = x² – x – 6 and g(x) = x – 3, find:
(f + g)(x)
(f – g)(x)
(fg)(x)
𝑓 𝑔 (𝑥)
𝑔 𝑓 (𝑥)

3. Lesson 2: Finding the Domain
Find the domain for D and E from the previous lesson. (Hint: Use the domain that works for functions before simplifying. )
D. 𝑓 𝑔 (𝑥) = x + 2, Domain:
E. 𝑔 𝑓 (𝑥) = 1 𝑥+2 , Domain:

4. Lesson 3: Composition of Functions
Given f(x) = |x| and g(x) = x³ – 2, find:
(f ◦ g)(x)
(g ◦ f)(x)
(f ◦ g)(-2)
(g ◦ f)(-2)

5. Lesson 4: Decomposing a Composite Function
Find two functions f and g such that (f ◦ g)(x) = h(x), where h(x) = − 𝑥 5 .

6. Lesson 5: Real-Life App – Cost of Widgets
The weekly cost of producing x units of widgets in a manufacturing process is given by the function C(x) = 48x The number of units produced in t hours is given by x(t) = 40t. Find and interpret (C ◦ x)(t).

7. 1.8: DIGI Yes or No
Given f(x) = 2x + 1 and g(x) = x² + 2x – 1, find:
(f – g)(x)
𝑓 𝑔 (𝑥)
(g ◦ f)(x)
(g ◦ f)(-3)
Write the function h(x) = 1 (𝑥 −2)² as a composition of two functions. h(x) = (f ◦ g)(x).