# Worksheet: Inverse of a Function

In this worksheet, we will practice finding the inverse of a function by changing the subject of the formula.

Q1:

Determine the inverse of .

• A
• B
• C
• D

Q2:

Find the inverse of the function .

• A
• B
• C
• D
• E

Q3:

Find the inverse of the function .

• A
• B
• C
• D
• E

Q4:

Determine the inverse function of , where .

• A
• B
• C
• D
• E

Q5:

Find the inverse of the function .

• A
• B
• C
• D
• E

Q6:

Solve .

• A
• B
• C
• D
• EThis has no solution.

Q7:

Jacob is trying to find the inverse of . He sets and then finds and then . What does Jacob determine to be?

• A
• B
• C
• D
• E

Q8:

Let and . Is it true that is the inverse of and is the inverse of ?

• Ayes
• Bno

Q9:

Find the inverse of the function .

• A
• B
• C
• D
• E

Q10:

What is the inverse of the function ?

• A
• B
• C
• D
• E

Q11:

Determine the domain on which the function has an inverse.

• A
• B or
• C
• D
• E

Q12:

If is the inverse function of the function then which of the following statements is true?

• Arange of domain of
• Bdomain of range of
• Cdomain of domain of
• Drange of range of
• Edomain of range of

Q13:

Find the inverse of the function .

• A where
• B where
• C where
• D where
• E where

Q14:

Find the inverse of the function , where .

• A
• B
• C
• D
• E

Q15:

Find for and state the domain.

• A for
• B for
• C for
• D for

Q16:

Find for .

• A
• B
• C
• D

Q17:

The period , in seconds, of a simple pendulum as a function of its length , in feet, is given by . Express as a function of , and determine the length of a pendulum with a period of 2 seconds.

• A, 3.26 feet
• B, 0.15 feet
• C, 20.5 feet
• D, 10.2 feet
• E, 0.39 feet

Q18:

The figure below represents the function . Find the value of . • A10
• B13
• C8
• D4

Q19:

For what numbers can we solve ?

• A
• B
• Cany
• D
• E

Q20:

The solid part of the following graph of shows how we can restrict the domain to obtain an inverse. What is the domain of the inverse?

• A
• B
• C
• D
• E

What is the range of the inverse?

• A
• B
• C
• D
• E

Give a formula for the inverse.

• A
• B
• C
• D
• E

Q21:

The following tables are partially filled for functions and that are inverses of each other. Determine the values of , , , , and .

 𝑥 𝑓(𝑥) 1 2 3 4 𝑑 6 −31 𝑎 −19 −10 1 14
 𝑥 𝑔(𝑥) −31 −26 −19 −10 1 𝑒 1 2 𝑏 𝑐 5 6
• A, , , ,
• B, , , ,
• C, , , ,
• D, , , ,
• E, , , ,

Q22:

A car travels at a constant speed of 50 miles per hour. The distance the car travels in miles is a function of time, , given in hours by . Find the inverse function expressing the time of travel in terms of the distance traveled. Find .

• A, 3.6 hours
• B, 0.13889 hours
• C, 0.2778 hours
• D, 7.2 hours
• E, 0.2778 hours

Q23:

Use the table to find .

 𝑥 ℎ(𝑥) 15 30 45 60 20 25 30 35

Q24:

Does the function , where , have an inverse?

• Ayes
• Bno

Q25:

Which of the following pairs of functions are inverses for all ?

• A,
• B,
• C,
• D,