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7.7 Operations on Functions

7.7 Operations on Functions. Composition of Functions. A new way of writing Operations with functions. Adding Subtracting Multiplication Division . Given. Find . Given. Find . Given. Find . Given. Find . Given. Find . Given. Find . Given. Find . Given. Find .

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7.7 Operations on Functions

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  1. 7.7 Operations on Functions Composition of Functions

  2. A new way of writing Operations with functions Adding Subtracting Multiplication Division

  3. Given Find

  4. Given Find

  5. Given Find

  6. Given Find

  7. Given Find

  8. Given Find

  9. Given Find

  10. Given Find

  11. Given Find

  12. Composition of Functions Combining two functions into one function. Where the answers to one function is the input to the other function. Given two Functions. f(x) = 2x + 1 g(x) = x – 3 f(g(x))=2(x – 3)+1 f(g(x))=2x – 6+1= 2x - 5 Where ever there is an x, put the other function

  13. Composition of Functions Given two Functions. f(x) = 2x + 1 g(x) = x – 3 f(g(x))=2(x – 3)+1 f(g(x))=2x – 6+1= 2x – 5 g(f(x))=(2x + 1) – 3 = 2x - 2

  14. Composition of Functions“The Books Notation” Given two Functions. f(x) = 2x + 1 g(x) = x – 3 f(g(x))=2(x – 3)+1 [f○ g](x) f(g(x))=2x – 6+1= 2x – 5 [f○ g](x)= 2x - 5 g(f(x))=(2x + 1) – 3 = 2x - 2 [g ○ f ](x) = 2x - 2

  15. Find [ f ○ g](x) and [ g ○ f ](x) for x = -2 f(x) = 3x2 – x + 4; g(x) = 2x – 1 [ f ○ g](x) find g(-2) = 2(-2) – 1 = -5 find f(-5)

  16. Find [ f ○ g](x) and [ g ○ f ](x) for x = -2 f(x) = 3x2 – x + 4; g(x) = 2x – 1 [ f ○ g](x) find g(-2) = 2(-2) – 1 = -5 find f(-5) = 3(-5)2 – (-5) + 4 =3(25) + 5 + 4 =75 + 5 +4 = 84

  17. Find [ f ○ g](x) and [ g ○ f ](x) for x = -2 f(x) = 3x2 – x + 4; g(x) = 2x – 1 [ g ○ f](x) find f(-2) = 3(-2)2 – (-2) + 4 =3(4) + 2 + 4 =12 + 2 + 4 = 18 find g(18) =

  18. Find [ f ○ g](x) and [ g ○ f ](x) for x = -2 f(x) = 3x2 – x + 4; g(x) = 2x – 1 [ g ○ f](x) find f(-2) = 3(-2)2 – (-2) + 4 =3(4) + 2 + 4 =12 + 2 + 4 = 18 find g(18) = 2(18) - 1 =36 - 1 =35

  19. Homework Page 387 – 388 # 17, 20, 31, 32, 35 – 43 odd

  20. Homework Page 387 – 388 # 18, 21, 33, 36 – 44 even

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