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) = x3 - 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) = 6x3 + 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) = x3 - 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) = x3 + 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) = x3 + 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
