1 4 building functions from functions
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1.4 building functions from functions. 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.

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operations w functions
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
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)

examples1
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
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

examples2
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
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
Homework
  • P. 116-117 #1-7 odd, 11-27 odd
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