COMPOSITE FUNCTIONS.pptx

presentation of a composite function

1. COMPOSITE FUNCTIONS 3. performs composition of functions

2. Definition: The composition of the function “f ○ g ” is defined as follows:

3. Examples:

4. Examples:

5. Examples:

6. Examples:

7. Examples:

8. Activity: Evaluate the following composition of functions. Given : f(x) = 2x + 1 & g(x) = 5x 2 (𝑓 ∘ 𝑔)(𝑥) (𝑔 ∘𝑓)(𝑥)

9. Activity: Evaluate the following composition of functions. Given : f(x) = 2x + 1 g(x) = 5x 2 (𝑓 ∘ 𝑔)(𝑥) (𝑔 ∘𝑓)(𝑥) Output Presentation

10. Activity: Evaluate the following composition of functions. Given : f(x) = 2x + 1 g(x) = 5x 2 (𝑓 ∘ 𝑔)(𝑥) (𝑔 ∘𝑓)(𝑥 )

11. Question: How to solve composite functions?

12. Try these: Evaluate the following composition of functions. Given : 𝑓(𝑥) = 2𝑥 + 1 ; g(x) = 5x 2 ; ℎ(𝑥) = 𝑥 + 3 (g ∘ h)(𝑥) (f ∘ h)(𝑥)

13. Answer: Evaluate the following composition of functions. Given : 𝑓(𝑥) = 2𝑥 + 1 ; g(x) = 5x 2 ; ℎ(𝑥) = 𝑥 + 3 (g ∘ h)(𝑥) (f ∘ h)(𝑥)

14. Assignment: Express each situation as a function of the variable being described. Let x represent the price of a book. Give a function f that represents the price of the book if a P100 price reduction applies. Give a function g that represents the price of the book if a 10% discount applies. Compute (𝑓 ∘ 𝑔)(𝑥) and (𝑔 ∘ 𝑓)(𝑥). Describe what these mean. Which of these give a better deal for the customer?