Solved Examples and Worksheet for Finding the Inverse of a Functions

Q1Find the inverse of the function {(4, 7), (7, 5), (8, 8)}.
A. {(7, 4), (5, 7), (8, 8)}
B. {(7, 4), (5, 7), (- 8, 8)}
C. {(4, 7), (7, 5), (8, 8)}
D. {(7, 4), (- 7, 5), (8, 8)}

Solutions
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Step: 1
The given function is {(4, 7), (7, 5), (8, 8)}.
Step: 2
Interchange the first and second co-ordinates in each pair.
Step: 3
The inverse of the function is {(7, 4), (5, 7), (8, 8)}.
Correct Answer is :   {(7, 4), (5, 7), (8, 8)}
Q2Find the inverse of the function {(- 6, - 3), (- 9, - 2), (- 12, - 5)}.
A. {(- 6, - 3), (- 9, - 2), (- 12, - 5)}
B. {(- 3, - 6), (- 2, - 9), (- 5, - 12)}
C. {(- 3, - 6), (2, - 9), (- 5, - 12)}
D. {(- 3, - 6), (- 9, - 2), (5, 12)}

Solutions
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Step: 1
The given function is {(- 6, - 3), (- 9, - 2), (- 12, - 5)}.
Step: 2
Interchange the first and second co-ordinates in each pair.
Step: 3
The inverse of the function is {(- 3, - 6), (- 2, - 9), (- 5, - 12)}.
Correct Answer is :   {(- 3, - 6), (- 2, - 9), (- 5, - 12)}
Q3Find the inverse of the function y = 7x + 9.
A. y = x - 97
B. y = - 7x + 9
C. y = x + 97
D. y = - 7x - 9

Solutions
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Step: 1
y = 7x + 9
Step: 2
Interchange x and y and find y in terms of x.
Step: 3
x = 7y + 9
  [Interchange x and y.]
Step: 4
x - 9 = 7y
  [Subtract 9 from the two sides of the equation.]
Step: 5
x - 97 = y
  [Divide throughout by 7.]
Step: 6
y = x - 97
Step: 7
The inverse function is y = x - 97.
Correct Answer is :    y = x - 97
Q4Find the inverse of the function y = - 815x + 2.

A. y = 158 x - 2
B. y = 30 - 15x8
C. y = 815x + 2
D. y = 15x - 308

Solutions
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Step: 1
y = - 815x + 2.
Step: 2
Interchange x and y and find y in terms of x.
Step: 3
x = - 815y + 2
  [Interchange x and y.]
Step: 4
x - 2 = - 815y
  [Subtracting 2 from the two sides of the equation.]
Step: 5
15(x - 2) = - 8y
  [Multiply.]
Step: 6
30 - 15x8 = y
  [Divide throughout by - 8.]
Step: 7
So, the inverse function is y = 30 - 15x8.
Correct Answer is :    y = 30 - 15x8
Q5Find the inverse of the function, y = 8x - 15, x = 8, 9, 10.
A. {(49, 8), (57, 9) (10, 65)}
B. {(49, 8), (9, 57) (65, 10)}
C. {(8, 49), (9, 57) (10, 65)}
D. {(49, 8), (57, 9) (65, 10)}

Solutions
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Step: 1
y = 8x - 15
Step: 2
y = 8(8) - 15 = 49
  [Substitute the values.]
Step: 3
y = 8(9) - 15 = 57
  [Substitute the values.]
Step: 4
y = 8(10) - 15 = 65
  [Substitute the values.]
Step: 5
The function is {(8, 49), (9, 57), (10, 65)}.
Step: 6
The inverse of the function is {(49, 8), (57, 9) (65, 10)}.
  [Interchange the first and second co-ordinates.]
Correct Answer is :    {(49, 8), (57, 9) (65, 10)}
Q6Find the inverse of the function {(- 5, - 4), (- 6, - 2), (- 7, - 5)}.

A. {(- 4, - 5), (- 2, - 6), (- 5, - 7)}
B. {(- 4, - 5), (- 6, - 2), (5, 7)}
C. {(- 4, - 5), (2, - 6), (- 5, - 7)}
D. {(- 5, - 4), (- 6, - 2), (- 7, - 5)}

Solutions
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Step: 1
The given function is {(- 5, - 4), (- 6, - 2), (- 7, - 5)}.
Step: 2
Interchange the first and second co-ordinates in each pair.
Step: 3
The inverse of the function is {(- 4, - 5), (- 2, - 6), (- 5, - 7)}.
Correct Answer is :   {(- 4, - 5), (- 2, - 6), (- 5, - 7)}
Q7Find the inverse of the function y = - 35x + 3.
A. y = 5x - 153
B. y = 53x - 3
C. y = 35x + 3
D. y = 15 - 5x3

Solutions
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Step: 1
y = - 35x + 3.
Step: 2
Interchange x and y and find y in terms of x.
Step: 3
x = - 35y + 3
  [Interchange x and y.]
Step: 4
x - 3 = - 35y
Step: 5
5(x - 3) = - 3y
  [Multiply.]
Step: 6
15 - 5x3 = y
  [Divide throughout by - 3.]
Step: 7
So, the inverse function is y = 15 - 5x3.
Correct Answer is :    y = 15 - 5x3
Q8Find the inverse of the function, y = - x - 16, x = - 8, - 9, - 10.

A. {(- 8, - 8), (- 9, - 7), (- 10, - 6)}
B. {(- 8, 8), (- 9, 7), (- 10, 6)}
C. {(- 8, - 8), (- 7, - 9), (10, - 6)}
D. {(- 8, - 8), (- 7, - 9), (- 6, - 10)}

Solutions
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Step: 1
y = - x - 16
Step: 2
y = - (- 8) - 16 = - 8
  [Substitute the values.]
Step: 3
y = - (- 9) - 16 = - 7
  [Substitute the values.]
Step: 4
y = - (- 10) - 16 = - 6
  [Substitute the values.]
Step: 5
The function is {(- 8, - 8), (- 9, - 7), (- 10, - 6)}.
Step: 6
The inverse of the function is {(- 8, - 8), (- 7, - 9), (- 6, - 10)}.
  [Interchange the first and second co-ordinates.]
Correct Answer is :   {(- 8, - 8), (- 7, - 9), (- 6, - 10)}
Q9The formula for the volume of a cube is z = l3. Find the inverse of this function.
A. z = l3
B. z = l3
C. z = l3
D. z = 3l

Solutions
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Step: 1
z = l3
Step: 2
To find the inverse of the function, interchange z and l and solve for z.
Step: 3
l = z3
  [Interchange l and z.]
Step: 4
l3 = z
  [Take cube root on each side.]
Step: 5
The inverse of the original function is z = l3.
Correct Answer is :    z = l3
Q10Find the inverse of the function y = 7x - 134.

A. y = - 7x + 134
B. y = 7x - 413
C. y = 4x + 137
D. y = 4x - 137

Solutions
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Step: 1
y = 7x - 134.
Step: 2
Interchange x and y and find y in terms of x.
Step: 3
x = 7y - 134
  [Interchange x and y.]
Step: 4
4x = 7y - 13
  [Multiply throughout by 5.]
Step: 5
4x + 13 = 7y
  [Add 15 to both sides of the equation.]
Step: 6
4x + 137 = y
Step: 7
The inverse function is y = 4x + 137.
Correct Answer is :    y = 4x + 137
Q11Find the inverse of the function, y = 8x - 15, x = 7, 8, 9.
A. {(41, 7), (49, 8) (57, 9)}
B. {(41, 7), (49, 8) (9, 57)}
C. {(7, 41), (8, 49) (9, 57)}
D. {(41, 7), (8, 49) (57, 9)}

Solutions
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Step: 1
y = 8x - 15
Step: 2
y = 8(7) - 15 = 41
  [Substitute the values.]
Step: 3
y = 8(8) - 15 = 49
  [Substitute the values.]
Step: 4
y = 8(9) - 15 = 57
  [Substitute the values.]
Step: 5
The function is {(7, 41), (8, 49), (9, 57)}.
Step: 6
The inverse of the function is {(41, 7), (49, 8) (57, 9)}.
  [Interchange the first and second co-ordinates.]
Correct Answer is :    {(41, 7), (49, 8) (57, 9)}
Q12Find the inverse of f(x) = x - 4x + 4 where x ≠ - 4.
A. y = - 2(x + 1x - 1) , x = 1
B. y = - 2(x + 1x - 1) , x ≠ 1
C. y = - 4(x + 1x - 1) , x ≠ 1
D. y = - 4(x + 1x - 1) , x = 1

Solutions
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Step: 1
Given, the restriction on the domain is x doesn't equal to -4.
Step: 2
f(x) = x - 4x + 4, x ≠ - 4
Step: 3
y = x - 4x + 4
Step: 4
x = y - 4y + 4
  [Interchange both x and y]
Step: 5
x(y + 4) = y - 4
Step: 6
xy + 4x = y - 4
Step: 7
xy - y = - 4x - 4
Step: 8
y(x - 1) = - 4(x + 1)
Step: 9
y = - 4(x + 1x - 1), x ≠ 1
Step: 10
The inverse of the function is y = - 4(x + 1x - 1), restricted the domain at x ≠ 1
Correct Answer is :   y = - 4(x + 1x - 1) , x ≠ 1

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