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Worksheet: Inverse of a Function
Q9:
Find for and state the domain.
- A for
- B for
- C for
- D for
Q10:
Find for .
- A
- B
- C
- D
Q11:
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
Q12:
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
Q13:
Use the table to find .
| 15 | 30 | 45 | 60 | |
| 20 | 25 | 30 | 35 |
Q14:
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
Q15:
Jacob is trying to find the inverse of . He sets and then finds and then . What does Tom determine to be?
- A
- B
- C
- D
- E
Q16:
Does the function , where , have an inverse?
- Ayes
- Bno
Q17:
Which of the following pairs of functions are inverses for all ?
- A ,
- B ,
- C ,
- D ,
Q18:
Which of the following functions does not have an inverse over its whole domain?
- A
- B
- C
- D
Q19:
Solve .
- A
- B
- C
- D This has no solution.
- E
Q20:
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
Q21:
Find the inverse of the function , where .
- A
- B
- C
- D
- E
Q22:
For what numbers can we solve ?
- A
- B
- C
- D any
- E
Q23:
The figure below represents the function . Find the value of .
Q24:
Find the inverse of the function .
- A
- B
- C
- D
- E
Q25:
Find the inverse of the function .
- A where
- B where
- C where
- D where
- E where