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# Composite Functions Composite Functions

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1. Composite Functions Composite Functions

2. What is to be Learned • What a composite function is • How to express a composite function

3. Definition • A number (or letter) is affected by more than one function

4. f(x) = 3x and g(x) = x2 Combining these: Multiply by 3, then square or Square, then multiply by 3 Not the same! Multiply by 3 Square

5. f( ) ? f(4) f( ) f(4) 16 f(x) = x2 f(4) = 16 f(16) = 162

6. With Formulas f(x)= 2x + 1 g(x) = 4x Composite functions f(g(x)) or f(g(x)) g(f(x)) Change this

7. f(x)= 2x + 1 g(x) = 4x Composite functions f(g(x)) or f(g(x)) g(f(x)) Change this

8. f(x)= 2x + 1 g(x) = 4x Composite functions f(g(x)) or f(g(x)) = f(4x) g(f(x)) Change this

9. f(x)= 2x + 1g(x) = 4x Composite functions f(g(x)) or f(g(x)) = f(4x) g(f(x)) Change this = 2(4x) + 1 = 8x + 1

10. f(x)= 2x + 1 g(x) = 4x Composite functions f(g(x)) or f(g(x)) = f(4x) g(f(x)) Change this g(f(x)) = 2(4x) + 1 = 8x + 1

11. f(x)= 2x + 1 g(x) = 4x Composite functions f(g(x)) or f(g(x)) = f(4x) g(f(x)) g(f(x)) = g(2x + 1) = 2(4x) + 1 = 8x + 1

12. f(x)= 2x + 1g(x) = 4x Composite functions f(g(x)) or f(g(x)) = f(4x) g(f(x)) g(f(x)) = g(2x + 1) = 4(2x +1) = 2(4x) + 1 = 8x + 1 = 8x + 4

13. Composite Functions Combination of more than one function. If f(x) = 4x and g(x) = x2 g( f(3) )? f(3) = 12 so g( f(3) ) = g (12 ) = = 144 122

14. f(x)= 3x + 4 g(x) = 2x Composite functions f(g(x)) or f(g(x)) = f(2x) g(f(x)) g(f(x)) = g(3x + 4) = 2(3x +4) = 3(2x) + 4 = 6x + 4 = 6x + 8