Inverse Functions Worksheet

Inverse Functions Worksheet
  • Page 1
 1.  
Find the inverse of the function {(- 6, - 4), (- 8, - 4), (- 10, - 3)}.
a.
{(- 4, - 6), (4, - 8), (- 3, - 10)}
b.
{(- 4, - 6), (- 8, - 4), (3, 10)}
c.
{(- 6, - 4), (- 8, - 4), (- 10, - 3)}
d.
{(- 4, - 6), (- 4, - 8), (- 3, - 10)}


Solution:

The given function is {(- 6, - 4), (- 8, - 4), (- 10, - 3)}.

Interchange the first and second co-ordinates in each pair.

The inverse of the function is {(- 4, - 6), (- 4, - 8), (- 3, - 10)}.


Correct answer : (4)
 2.  
Find the inverse of the function y = 4x + 8.
a.
y = x + 84
b.
y = - 4x - 8
c.
y = x - 84
d.
y = - 4x + 8


Solution:

y = 4x + 8

Interchange x and y and find y in terms of x.

x = 4y + 8
[Interchange x and y.]

x - 8 = 4y
[Subtract 8 from the two sides of the equation.]

x - 84 = y
[Divide throughout by 4.]

y = x - 84

The inverse function is y = x - 84.


Correct answer : (3)
 3.  
Find the inverse of the function y = 4x - 74.
a.
y = 4x + 74
b.
y = x + 7
c.
y = 44x + 7
d.
y = 4x + 3


Solution:

y = 4x - 74.

Interchange x and y and find y in terms of x.

x = 4y - 74
[Interchange x and y.]

4x = 4y - 7
[Multiply throughout by 4.]

4x + 7 = 4y
[Add 7 to both sides of the equation.]

4x + 74 = y

The inverse function is y = 4x + 74.


Correct answer : (1)
 4.  
The formula for the volume of a cube is x = t3. Find the inverse of this function.
a.
x = 3t
b.
x = t3
c.
x = t3
d.
x = t3


Solution:

x = t3

To find the inverse of the function, interchange x and t and solve for x.

t = x3
[Interchange t and x.]

t3 = x
[Take cube root on each side.]

The inverse of the original function is x = t3.


Correct answer : (4)
 5.  
Find the inverse of the function y = - 6 11x + 3.
a.
y = 11x - 336
b.
y = 33 - 11x6
c.
y = 6 11x + 3
d.
y = 11 6 x - 3


Solution:

y = - 6 / 11x + 3.

Interchange x and y and find y in terms of x.

x = - 6 / 11y + 3
[Interchange x and y.]

x - 3 = - 6 / 11y
[Subtracting 3 from the two sides of the equation.]

11(x - 3) = - 6y
[Multiply.]

33 - 11x6 = y
[Divide throughout by - 6.]

So, the inverse function is y = 33 - 11x6.


Correct answer : (2)
 6.  
Find the domain and range of inverse of the function {(4, 2), (5, 2), (6, 3), (7, 5)}.
a.
Domain: {2, 3, 5}, Range: {4, 5, 6, 7}
b.
Domain: {2, 3, 6}, Range: {4, 5, 6, 7}
c.
Domain: {2, 3, 5}, Range: {4, 5, 7, 7}
d.
Domain: {2, 2, 5}, Range: {4, 5, 6, 6}


Solution:

{(4, 2), (5, 2), (6, 3), (7, 5)}.

Interchange the first and second co-ordinates in each pair.

The inverse of the function is {(2, 4), (2, 5), (3, 6), (5, 7)}.

Domain: {2, 3, 5} and Range: {4, 5, 6, 7}.


Correct answer : (1)
 7.  
Find the domain of f - 1, where y = f(x) = 8x - 5, x ≠ 5.
a.
{x: x is real}
b.
{x: x is real except 5}
c.
{x: x is real except 8}
d.
{x: x is real except zero}


Solution:

y = 8x - 5

Interchange x and y and find y interms of x.

x = 8y - 5
[Interchange x and y.]

x (y - 5) = 8
[Multiply throughout by (y - 5) .]

y - 5 = 8x
[Divide throughout by x.]

y = 8x + 5
[Add 5 to both sides of the equation.]

So, the inverse function f - 1 is y = 8x + 5.

Domain of a function is the set of values used as input to the function.

Domain of f - 1 : {x: x is real except zero}.


Correct answer : (4)
 8.  
Find the range of f - 1, where y = f (x) = 6x.
a.
{x: x is real except 6}
b.
{x: x is real except zero}
c.
{x: x is real}
d.
{x: x ≥ 0 }


Solution:

y = 6x

Interchange x and y and find y in terms of x.

x = 6y
[Interchange x and y.]

x2 = 6y
[Square each side of the equation.]

The inverse of the function f -1 is, y = x26.

Range of a function is a set values that are output by the function.

Range of f -1: {x: x ≥ 0}.


Correct answer : (4)
 9.  
Find the range of inverse of the function {(s, - 8), (k, - 9), (y, - 4), (z, - 3)}.
a.
Range: {- 8, - 9, - 4, - 3}
b.
Range: {8, 9, 4, 3}
c.
Range: {s, k, y, z}
d.
Range: {- s, - k, - y, - z}


Solution:

{(s, - 8), (k, - 9), (y, - 4), (z, - 3)}

Interchange the first and second co-ordinates in each pair.

Inverse of the function is {(- 8, s), (- 9, k), (- 4, y), (- 3, z)}.

Range : {s, k, y, z}.


Correct answer : (3)
 10.  
Find the domain and range of inverse of the function {(5, 5), (7, 5), (8, 7), (10, 10)}.
a.
Domain: {5, 7, 10} and Range: {6, 7, 8, 10}
b.
Domain: {5, 7, 8, 10} and Range: {5, 7, 10}
c.
Domain: {5, 7, 8, 11} and Range: {5, 7, 10}
d.
Domain: {5, 7, 10} and Range: {5, 7, 8, 10}


Solution:

{(5, 5), (7, 5), (8, 7), (10, 10)}

Interchange the first and second co-ordinates in each pair.

Inverse of the function is {(5, 5), (5, 7), (7, 8), (10, 10)}.

Domain : {5, 7, 10} and Range :{ 5, 7, 8, 10}


Correct answer : (4)

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