General Mathematics - Composition of Functions
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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.
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General Mathematics - Composition of Functions
- 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 )