The document discusses composite functions and provides examples of evaluating composite functions. Composite functions are defined as the composition of two functions f and g, written as f ∘ g, where g is applied first and then f is applied to the output of g. Examples are provided of evaluating composite functions where the inner and outer functions are given.

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) = 5x2
1.(𝑓 ∘ 𝑔)(𝑥)
2. (𝑔 ∘𝑓)(𝑥)

9. Activity:
Evaluate the following composition of functions.
Given : f(x) = 2x + 1 g(x) = 5x2
1.(𝑓 ∘ 𝑔)(𝑥)
2. (𝑔 ∘𝑓)(𝑥)
Output Presentation

10. Activity:
Evaluate the following composition of functions.
Given : f(x) = 2x + 1 g(x) = 5x2
1. (𝑓 ∘ 𝑔)(𝑥)
2. (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) = 5x2 ; ℎ(𝑥) = 𝑥 + 3
1.(g ∘ h)(𝑥)
2. (f ∘ h)(𝑥)

13. Answer:
Evaluate the following composition of functions.
Given : 𝑓(𝑥) = 2𝑥 + 1; g(x) = 5x2 ; ℎ(𝑥) = 𝑥 + 3
1. (g ∘ h)(𝑥)
2. (f ∘ h)(𝑥)

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