The document discusses the composition of functions in mathematics, defining it as the application of one function to another to yield a result. It provides examples and exercises for evaluating composite functions, including specific function pairings and operations. Key operations are demonstrated with multiple functional expressions and their evaluations.

1. COMPOSITION OF FUNCTIONS
General Mathematics

2. Learning Competencies:
 Defines composition of functions
 Performs composition of functions
 Evaluates functional problems using composition of
functions

3. Composition of Functions
 Operation of function that must have two functions
namely: f(x) and g(x), and then perform the indicated
operation to produce the result: h(x)
 Also defined as “applying a function to the other function”

5. Composition of Functions
𝑓 𝑥 = 3𝑥 − 1; 𝑔 𝑥 = 𝑥 + 4
𝐹𝑖𝑛𝑑 𝑓 ○ 𝑔

6. Composition of Functions
𝑓 𝑥 = 3𝑥 − 1; 𝑔 𝑥 = 𝑥 + 4
𝑓 ○ 𝑔 = 3 𝑥 + 4 − 1
𝑓 ○ 𝑔 = 3𝑥 + 12 − 1
𝑓 ○ 𝑔 = 3𝑥 + 11

7. EXERCISE!
DIRECTIONS: Evaluate the given composite functions
𝑓 𝑥 = 𝑥2
− 6; 𝑔 𝑥 = 𝑥 + 4
𝑓 𝑥 = 𝑥 + 3; 𝑔 𝑥 = 𝑥 − 9
𝑓 𝑥 = 2𝑥 + 4; 𝑔 𝑥 = 8 − 3𝑥

8. Composition of Functions
𝑓 𝑥 =
1
2
𝑥 − 4; 𝑔 𝑥 = 𝑥 + 3
𝐹𝑖𝑛𝑑 𝑓 ○ 𝑔

9. Composition of Functions
𝑓 𝑥 =
1
2
𝑥 − 4; 𝑔 𝑥 = 𝑥 + 3
f ○ 𝑔 =
1
2
𝑥 + 3 − 4
𝑓 ○ 𝑔 = 2
1
2
𝑥 + 3 − 4 2
𝑓 ○ 𝑔 = 𝑥 + 3 − 8
𝑓 ○ 𝑔 = 𝑥 − 5

10. Composition of Functions
𝑓 𝑥 =
2
𝑥 + 3
; 𝑔 𝑥 =
−3𝑥 − 2
𝑥
𝐹𝑖𝑛𝑑 𝑓 ○ 𝑔

12. Composition of Functions
𝑓 𝑥 = 4𝑥 + 3; 𝑔 𝑥 = 𝑥 − 2
𝐹𝑖𝑛𝑑 𝑓(𝑔 5 )

13. Composition of Functions
𝑓 𝑥 = 4𝑥 + 3; 𝑔 𝑥 = 𝑥 − 2
𝑓 𝑔 5 = 4 5 − 2 + 3
𝑓 𝑔 5 = 4 3 + 3
𝑓 𝑔 5 = 12 + 3
𝑓 𝑔 5 = 15

14. Composition of Functions
𝑓 𝑥 = 6𝑥 − 4; 𝑔 𝑥 = 𝑥 − 8
𝐹𝑖𝑛𝑑 𝑓(𝑔 9 )

15. Composition of Functions
𝑓 𝑥 = 6𝑥 − 4; 𝑔 𝑥 = 𝑥 − 8
𝑓 𝑔 9 = 6 9 − 8 − 4
𝑓 𝑔 9 = 6 1 − 4
𝑓 𝑔 9 = 6 − 4
𝑓 𝑔 9 = 2

16. EXERCISE!
DIRECTIONS: Evaluate the given composite functions
𝑓 𝑥 = 𝑥2
+ 7; 𝑔 𝑥 = 𝑥 − 3: 𝐹𝑖𝑛𝑑 𝑓(𝑔 3 )
𝑓 𝑥 = 𝑥 + 3; 𝑔 𝑥 = 𝑥 − 5: 𝐹𝑖𝑛𝑑 𝑔 ○ 𝑓
𝑓 𝑥 =
1
4
𝑥 + 6; 𝑔 𝑥 = 𝑥 + 4: 𝐹𝑖𝑛𝑑 𝑓 ○ 𝑔
𝑓 𝑥 = 7𝑥 + 4; 𝑔 𝑥 = 2𝑥 − 4: 𝐹𝑖𝑛𝑑 𝑔(𝑔 5 )