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Question : Graph the function as a solid curve and its inverse as a dashed curve. 49) f(x) = 2x : 2162218

Determine whether the function is one-to-one.

41) f(x) = (1/3)^{x}

A) No

B) Yes

Determine whether the given function is one-to-one. If so, find a formula for the inverse.

42) f(x) = 4x + 3

A) f^{-1}(x) = (x - 3/4)

B) Not a one-to-one function

C) f^{-1}(x) = (x/4) - 3

D) f^{-1}(x) = (x + 3/4)

43) f(x) = x^{3} - 8

A) f^{-1}(x) = (3)Ö(x) + 8

B) Not a one-to-one function

C) f^{-1}(x) = (3)Ö(x - 8)

D) f^{-1}(x) = (3)Ö(x + 8)

44) f(x) = 6x^{3} + 4

A) f^{-1}(x) = (3)Ö((x/6)) - 4

B) f^{-1}(x) = (3)Ö((x - 4/6))

C) Not a one-to-one function

D) f^{-1}(x) = (3)Ö((x + 4/6))

45) f(x) = (4/x + 5)

A) f^{-1}(x) = (5 + 4x/x)

B) Not a one-to-one function

C) f^{-1}(x) = (x/5 + 4x)

D) f^{-1}(x) = (-5x + 4/x)

46) f(x) = (3)Ö(x + 3)

A) f^{-1}(x) = (x + 3)^{3}

B) f^{-1}(x) = x^{3} - 3

C) f^{-1}(x) = (3)Ö(x - 3)

D) Not a one-to-one function

47) f(x) = (4x - 7/2x + 6)

A) f^{-1}(x) = (2x - 4/-6x - 7)

B) f^{-1}(x) = (-6x - 7/2x - 4)

C) Not a one-to-one function

D) f^{-1}(x) = (4x - 7/2x + 6)

48) f(x) = (x + 5)^{2}

A) f^{-1}(x) = √(x) - 5

B) f^{-1}(x) = (1/√(x - 5))

C) f^{-1}(x) = √(x - 5)

D) Not a one-to-one function

Graph the function as a solid curve and its inverse as a dashed curve.

49) f(x) = 2x

A)

B)

C)

D)

50) f(x) = (5/2)x + 4

A)

B)

C)

D)

51) f(x) = x^{3} + 4

A)

B)

C)

D)

Use composition to verify whether or not the inverse is correct.

52) f(x) = - (5/7)x, f^{-1}(x) = - (7/5)x

A) Yes

B) No

53) f(x) = 8x - 9, f^{-1}(x) = (x + 8/9)

A) Yes

B) No

54) f(x) = 7x - 7, f^{-1}(x) = (1/7)x + 1

A) Yes

B) No

55) f(x) = (4/x + 3), f^{-1}(x) = (3x + 4/x)

A) Yes

B) No

56) f(x) = 4x + 16, f^{-1}(x) = (1/4)x - 4

A) No

B) Yes

57) f(x) = 5x + 10, f^{-1}(x) = (1/5)x - 5

A) No

B) Yes

58) f(x) = x^{3} + 7, f^{-1}(x) = (3)Ö(x + 7)

A) Yes

B) No

Solve the problem.

59) A size 12 dress in Country C is size 44 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = x + 32. Find a formula for the inverse of the function described.

A) f^{-1}(x) = x - 32

B) f^{-1}(x) = (x/-32)

C) f^{-1}(x) = (x/32)

D) f^{-1}(x) = x + 32

60) A size -10 dress in Country C is size -10 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = x - 20. Find a formula for the inverse of the function described.

A) f^{-1}(x) = x + 20

B) f^{-1}(x) = (x/20)

C) f^{-1}(x) = (x/-20)

D) f^{-1}(x) = x - 20

61) A size 4 dress in Country C is size 32 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 12). Find a formula for the inverse of the function described.

A) f^{-1}(x) = x - 12

B) f^{-1}(x) = (x/2) - 12

C) f^{-1}(x) = (x/2) + 12

D) f^{-1}(x) = (x - 12/2)

62) A size 32 dress in Country C is size -4 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = (x/2) - 20. Find a formula for the inverse of the function described.

A) f^{-1}(x) = 2(x + 20)

B) f^{-1}(x) = x + 20

C) f^{-1}(x) = 2x + 20

D) f^{-1}(x) = 2(x - 20)

63) 32° Fahrenheit = 0° Celsius. A function that converts temperatures in Fahrenheit to those in Celsius is f(x) = (5/9)(x - 32) Fahrenheit. Find a formula for the inverse of the function described.

A) f^{-1}(x) = x + 32

B) f^{-1}(x) = (9/5)x - 32

C) f^{-1}(x) = (9/5)x + 32

D) f^{-1}(x) = (5/9)(x - 32)

64) An organization determines that the cost per person of chartering a bus is given by the formula

C(x) = (150 + 7x/x),

where x is the number of people in the group and C(x) is in dollars. Find a formula for the inverse of the function described.

A) C^{-1}(x) = (150/x - 7)

B) C^{-1}(x) = (150 + x/7)

C) C^{-1}(x) = (7/x - 150)

D) C^{-1}(x) = (150/x + 7)

65) A size 6 dress in Country C is size 26 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = x + 20. Find a formula for the inverse of the function described. Use the inverse function to find dress sizes in the Country C that correspond to the size of 28 in France.

A) (1/8)

B) (1/4)

C) 4

D) 8