# 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)}.

2.
Find the inverse of the function $y$ = 4$x$ + 8.
 a. $y$ = b. $y$ = - 4$x$ - 8 c. $y$ = d. $y$ = - 4$x$ + 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.

3.
Find the inverse of the function $y$ = .
 a. $y$ = b. $y$ = $x$ + 7 c. $y$ = d. $y$ = 4$x$ + 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.

4.
The formula for the volume of a cube is $x$ = $t$3. Find the inverse of this function.
 a. $x$ = 3$t$ b. $x$ = $\frac{t}{3}$ c. $x$ = $t$3 d. $x$ = $\sqrt[3]{t}$

#### 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.

5.
Find the inverse of the function $y$ = - $\frac{6}{11}$$x$ + 3.
 a. $y$ = b. $y$ = c. $y$ = $\frac{6}{11}$$x$ + 3 d. $y$ = $\frac{11}{6}$ $x$ - 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.

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}.

7.
Find the domain of $f$ - 1, where $y$ = $f$($x$) = , $x$ ≠ 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}.

8.
Find the range of $f$ - 1, where $y$ = $f$ ($x$) = $\sqrt{6x}$.
 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}.

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}.

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}