# Worksheet: Inverse of a Function

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

**Q5: **

Find the inverse of the function .

- A
- B
- C
- D
- E

**Q6: **

Solve .

- A
- B
- C
- D This has no solution.
- E

**Q7: **

Bassem is trying to find the inverse of . He sets and then finds and then . What does Bassem 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

**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
- C
- D or
- E

**Q12: **

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

- Arange of range of
- Bdomain of domain of
- Crange of domain of
- Ddomain 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 , 10.2 feet
- B , 20.5 feet
- C , 0.15 feet
- D , 3.26 feet
- E , 0.39 feet

**Q18: **

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

**Q19: **

For what numbers can we solve ?

- A
- B
- C
- D any
- 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 .

1 | 2 | 3 | 4 | 6 | ||

1 | 14 |

1 | ||||||

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 , 7.2 hours
- B , 0.2778 hours
- C , 0.13889 hours
- D , 3.6 hours
- E , 0.2778 hours

**Q23: **

Use the table to find .

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 ,