# Lesson Worksheet: Inverse of a Function Mathematics

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:

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

Q7:

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

• AYes
• BNo

Q8:

Find the inverse of the function .

• A
• B
• C
• D
• E

Q9:

What is the inverse of the function ?

• A
• B
• C
• D
• E

Q10:

Determine the domain on which the function has an inverse.

• A
• B or
• C
• D
• E

Q11:

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

Q12:

Find the inverse of the function .

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

Q13:

Find the inverse of the function , where .

• A
• B
• C
• D
• E

Q14:

Find for and state the domain.

• A for
• B for
• C for
• D for

Q15:

Find for .

• A
• B
• C
• D

Q16:

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

Q17:

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

Q18:

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, , , ,

Q19:

Does the function , where , have an inverse?

• AYes
• BNo

Q20:

The figure below represents the function . Find the value of . Q21:

Does every function which is strictly increasing on its domain have an inverse function?

• ANo
• BYes

Q22:

Find the inverse of the function represented by the following table:

 𝑥 𝑓(𝑥) −3 −1 1 3 16 19 112 115
• A
• B
• C
• D
• E

Q23:

Does an odd function always have an inverse function?

• AYes
• BNo

Q24:

Given that is the inverse of the function , what is the value of ?

Q25:

Does an even function always have an inverse function?

• ANo
• BYes