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7.7 Operations on Functions

7.7 Operations on Functions

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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

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  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