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?

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)

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:

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)

Lesson 4: Decomposing a Composite Function Find two functions f and g such that (f ◦ g)(x) = h(x), where h(x) = 3 8 − 𝑥 5 .

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 + 1150. The number of units produced in t hours is given by x(t) = 40t. Find and interpret (C ◦ x)(t).

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).