Let f ( x ) = 2 x 2 + x − 3 f open x close equals , 2 x squared , plus x minus 3  and g ( x ) = x − 1 . g open x close equals x minus 1 .  Perform each function operation and then find the domain.

21. ( f + g ) ( x ) open f plus g close open x close
22. ( f − g ) ( x ) open f minus g close open x close
23. ( g − f ) ( x ) open g minus f close open x close
24. ( f · g ) ( x ) open f middle dot g close open x close
25. f g ( x ) f over g . open x close
26. g f ( x ) g over f . open x close

See Problem 3.

Let g(x) = 2x and h ( x ) = x 2 + 4 . h open x close equals , x squared , plus 4 .  Find each value or expression.

27. ( h ∘ g ) ( 1 ) open h composition g close open 1 close
28. ( h ∘ g ) ( − 5 ) open h composition g close open negative 5 close
29. ( h ∘ g ) ( − 2 ) open h composition g close open negative 2 close
30. ( g ∘ h ) ( − 2 ) open g composition h close open negative 2 close
31. ( g ∘ h ) ( 0 ) open g composition h close open 0 close
32. ( g ∘ h ) ( a ) open g composition h close open eh close
33. ( g ∘ g ) ( a ) open g composition g close open eh close
34. ( h ∘ h ) ( a ) open h composition h close open eh close
35. ( h ∘ g ) ( a ) open h composition g close open eh close

Let f ( x ) = x 2 f open x close equals , x squared  and g ( x = ) x − 3 . g open x equals close x minus 3 .  Find each value or expression.

36. ( g ∘ f ) ( − 2 ) open g composition f close open negative 2 close
37. ( f ∘ g ) ( − 2 ) open f composition g close open negative 2 close
38. ( g ∘ f ) ( 0 ) open g composition f close open 0 close
39. ( f ∘ g ) ( 0 ) open f composition g close open 0 close
40. ( g ∘ f ) ( 3.5 ) open g composition f close open 3.5 close
41. ( f ∘ g ) ( 3.5 ) open f composition g close open 3.5 close
42. ( f ∘ g ) ( a ) open f composition g close open eh close
43. ( g ∘ f ) ( − a ) open g composition f close open negative eh close
44. ( f ∘ g ) ( − a ) open f composition g close open negative eh close

    See Problem 4.

45. Sales A computer store offers a 5% discount off the list price x for any computer bought with cash, rather than put on credit. At the same time, the manufacturer offers a $200 rebate for each purchase of a computer.

    1. Write a function f(x) to represent the price after the cash discount.
    2. Write a function g(x) to represent the price after the $200 rebate.
    3. Suppose the list price of a computer is $1500. Use a composite function to find the price of the computer if the discount is applied before the rebate.
    4. Suppose the list price of a computer is $1500. Use a composite function to find the price of the computer if the rebate is applied before the discount.
46. Economics Suppose the function f(x) = 0.15x represents the number of U.S. dollars equivalent to x Chinese yuan and the function g(y) = 14.07y represents the number of Mexican pesos equivalent to y U.S. dollars.
    1. Write a composite function that represents the number of Mexican pesos equivalent to x Chinese yuan.
    2. Find the value in Mexican pesos of an item that costs 15 Chinese yuan.

Let f ( x ) = 2 x + 5 f open x close equals 2 x plus 5  and g ( x ) = x 2 − 3 x + 2 . g open x close equals , x squared , minus 3 x plus 2 .  Perform each function operation and then find the domain.

47. f ( x ) + g ( x ) f open x close plus g open x close
48. 3 f ( x ) − 2 3 f open x close minus 2
49. g ( x ) − f ( x ) g open x close minus f open x close
50. − 2 g ( x ) + f ( x ) negative 2 g open x close plus f open x close
51. f ( x ) − g ( x ) + 10 f open x close minus g open x close plus 10
52. 4 f ( x ) + 2 g ( x ) 4 f open x close plus 2 g open x close
53. − f ( x ) + 4 g ( x ) negative f open x close plus 4 g open x close
54. f ( x ) − 2 g ( x ) f open x close minus 2 g open x close
55. f ( x ) ⋅ g ( x ) f open x close dot g open x close
56. − 3 f ( x ) ⋅ g ( x ) negative 3 f open x close dot g open x close
57. f ( x ) g ( x ) fraction f , open x close , over g , open x close end fraction
58. 5 f ( x ) g ( x ) fraction 5 f , open x close , over g , open x close end fraction

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