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1.4 building functions from functionsPowerPoint Presentation

1.4 building functions from functions

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Operations w/ functions

- Sum: (f + g)(x) = f(x) + g(x)
- difference: (f – g)(x) = f(x) – g(x)
- Product: (fg)(x) = f(x)g(x)
- Quotient: f (x) = f(x)
g g(x)

Examples

- For f(x) = 3x + 5, g(x) = 2x – 1, find the following with each domain.
- 1. f(x) + g(x)
- 2. f(x) – g(x)
- 3. f(x)g(x)
- 4. f(x)
g(x)

Examples

- For f(x) = 9x, g(x) = 4x2 – 2, find the following with each domain.
- 5. g(x) + f(x)
- 6. g(x) – f(x)
- 7. g(x)f(x)
- 8. g(x)
f(x)

Composition of functions

- Let f and g be 2 functions such that the domain of f intersects the range of g.
- (f◦g)(x) = f(g(x))
- How to do: all x values in the 1st function get replaced by the entire 2nd function
- Example: find (f◦g)(x) = f(g(x))
1.f(x) = 2x – 1, g(x) = 4x + 3

f(g(x)) = 2(4x + 3) – 1 = 8x + 5

g(f(x)) = 4(2x – 1) + 3 = 8x - 1

2. f(x) = ex, g(x) = √x

f(g(x)) = e√x

g(f(x)) = √ex

Examples

- Find f(g(x)) and g(f(x)) and state each domain
9. f(x) = 3x + 2, g(x) = x – 1

10. f(x) = x2 – 2, g(x) = x + 1

11. f(x) = 1 , g(x) = 1

2x 3x

Evaluating functions

- Perform each operation and then evaluate each for the given value
f(x) = 2x – 1, g(x) = x2

12. (f + g)(-2)

13. (f – g)(10)

14. (fg)(3)

15. g (-3)

f

16. (f◦g)(5)

17. (g◦f)(-4)

Homework

- P. 116-117 #1-7 odd, 11-27 odd

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