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7.1 – Operations on Functions

7.1 – Operations on Functions. Operation Definition. Operation Definition Sum . Operation Definition Sum ( f + g )( x ). Operation Definition Sum ( f + g )( x ) = f ( x ) + g ( x ). Operation Definition Sum ( f + g )( x ) = f ( x ) + g ( x )

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7.1 – Operations on Functions

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  1. 7.1 – Operations on Functions

  2. Operation Definition

  3. Operation Definition Sum

  4. Operation Definition Sum (f + g)(x)

  5. Operation Definition Sum (f + g)(x) = f(x) + g(x)

  6. Operation Definition Sum (f + g)(x) = f(x) + g(x) Difference

  7. Operation Definition Sum (f + g)(x) = f(x) + g(x) Difference (f – g)(x) =

  8. Operation Definition Sum (f + g)(x) = f(x) + g(x) Difference (f – g)(x) = f(x) – g(x)

  9. Operation Definition Sum (f + g)(x) = f(x) + g(x) Difference (f – g)(x) = f(x) – g(x) Product

  10. Operation Definition Sum (f + g)(x) = f(x) + g(x) Difference (f – g)(x) = f(x) – g(x) Product (f·g)(x) =

  11. Operation Definition Sum (f + g)(x) = f(x) + g(x) Difference (f – g)(x) = f(x) – g(x) Product (f·g)(x) = f(x) ·g(x)

  12. Operation Definition Sum (f + g)(x) = f(x) + g(x) Difference (f – g)(x) = f(x) – g(x) Product (f·g)(x) = f(x) ·g(x) Quotient f (x) = g

  13. Operation Definition Sum (f + g)(x) = f(x) + g(x) Difference (f – g)(x) = f(x) – g(x) Product (f·g)(x) = f(x) ·g(x) Quotient f (x) = f(x) gg(x)

  14. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9

  15. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x)

  16. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x) = f(x) + g(x)

  17. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x) = f(x) + g(x)

  18. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x) = f(x) + g(x) = (2x – 3)

  19. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x) = f(x) + g(x) = (2x – 3)

  20. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x) = f(x) + g(x) = (2x – 3) + (4x + 9)

  21. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x) = f(x) + g(x) = (2x – 3) + (4x + 9) = 6x + 6

  22. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x) = f(x) + g(x) = (2x – 3) + (4x + 9) = 6x – 6 (f – g)(x)

  23. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x) = f(x) + g(x) = (2x – 3) + (4x + 9) = 6x – 6 (f – g)(x) = f(x) – g(x)

  24. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x) = f(x) + g(x) = (2x – 3) + (4x + 9) = 6x – 6 (f – g)(x) = f(x) – g(x)

  25. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x) = f(x) + g(x) = (2x – 3) + (4x + 9) = 6x – 6 (f – g)(x) = f(x) – g(x) = (2x – 3)

  26. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x) = f(x) + g(x) = (2x – 3) + (4x + 9) = 6x – 6 (f – g)(x) = f(x) – g(x) = (2x – 3)

  27. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x) = f(x) + g(x) = (2x – 3) + (4x + 9) = 6x – 6 (f – g)(x) = f(x) – g(x) = (2x – 3) – (4x + 9)

  28. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x) = f(x) + g(x) = (2x – 3) + (4x + 9) = 6x – 6 (f – g)(x) = f(x) – g(x) = (2x – 3) – (4x + 9)

  29. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x) = f(x) + g(x) = (2x – 3) + (4x + 9) = 6x – 6 (f – g)(x) = f(x) – g(x) = (2x – 3) – (4x + 9) = 2x – 3 –4x

  30. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x) = f(x) + g(x) = (2x – 3) + (4x + 9) = 6x – 6 (f – g)(x) = f(x) – g(x) = (2x – 3) – (4x + 9) = 2x – 3 – 4x– 9

  31. Ex. 1 Find (f + g)(x), (f – g)(x), (f·g)(x), & f (x) for f(x) g and g(x) if f(x) = 2x – 3 and g(x) = 4x + 9 (f + g)(x) = f(x) + g(x) = (2x – 3) + (4x + 9) = 6x – 6 (f – g)(x) = f(x) – g(x) = (2x – 3) – (4x + 9) = 2x – 3 – 4x – 9 = -2x – 12

  32. (f·g)(x)

  33. (f·g)(x) = f(x) ·g(x)

  34. (f·g)(x) = f(x)·g(x)

  35. (f·g)(x) = f(x) ·g(x) = (2x – 3)

  36. (f·g)(x) = f(x) ·g(x) = (2x – 3)

  37. (f·g)(x) = f(x) ·g(x) = (2x – 3)(4x + 9)

  38. (f·g)(x) = f(x) ·g(x) = (2x – 3)(4x + 9) = 8x2+ 18x – 12x – 27

  39. (f·g)(x) = f(x) ·g(x) = (2x – 3)(4x + 9) = 8x2+ 18x – 12x – 27 = 8x2+ 6x – 27

  40. (f·g)(x) = f(x) ·g(x) = (2x – 3)(4x + 9) = 8x2+ 18x – 12x – 27 = 8x2+ 6x – 27 f (x) g

  41. (f·g)(x) = f(x) ·g(x) = (2x – 3)(4x + 9) = 8x2+ 18x – 12x – 27 = 8x2+ 6x – 27 f (x) = f(x) gg(x)

  42. (f·g)(x) = f(x) ·g(x) = (2x – 3)(4x + 9) = 8x2+ 18x – 12x – 27 = 8x2+ 6x – 27 f (x) = f(x) gg(x) = 2x – 3 4x + 9

  43. (f·g)(x) = f(x) ·g(x) = (2x – 3)(4x + 9) = 8x2+ 18x – 12x – 27 = 8x2+ 6x – 27 f (x) = f(x) gg(x) = 2x – 3 4x + 9 *Factor & Simplify if possible!

  44. Composite Function

  45. Composite Function - taking the function

  46. Composite Function - taking the function of a function

  47. Composite Function - taking the function of a function [f°g(x)]

  48. Composite Function - taking the function of a function [f°g(x)] = f[g(x)]

  49. Composite Function - taking the function of a function [f°g(x)] = f[g(x)] Ex. 2 Find [f°g(x)] and [g°f(x)] for the functions f(x) = x + 3 and g(x) = x2+ x – 1.

  50. Composite Function - taking the function of a function [f°g(x)] = f[g(x)] Ex. 2 Find [f°g(x)] and [g°f(x)] for the functions f(x) = x + 3 and g(x) = x2+ x – 1. [f°g(x)] = f[g(x)]

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