# Lesson Worksheet: Graphs of Inverses of Functions Mathematics

In this worksheet, we will practice using a graph to find the inverse of a function and analyzing the graphs for the inverse of a function.

**Q1: **

The following is the graph of .

Which one is the graph of the inverse function ?

- A(b)
- B(a)
- C(c)

**Q2: **

Consider the two following figures.

The first figure shows the graph of and a tangent to the graph with gradient 1. This tangent meets the graph at a point with -coordinate .

The second figure shows the graphs of and its inverse . The graphs cross in the third quadrant and touch in the first quadrant.

What is the value of ?

- A
- B
- C
- D
- E

What are the -coordinates of the two points of intersection of the graphs in the second figure?

- A and
- B and
- C and
- D and
- E and

**Q3: **

The graphs of and its inverse intersect at three points, one of which is .

Determine the value of .

- A
- B
- C
- D
- E

Find the of the point marked on the figure.

- A
- B
- C
- D
- E

Find the of the point marked on the figure.

- A
- B
- C
- D
- E

**Q4: **

Determine whether the inverse of the represented function is a function or not.

- ANot a function
- BA function

**Q5: **

In the given figure, the green points represent the function . Do the blue points represent ?

- ANo
- BYes

**Q6: **

By sketching the graphs of and for , determine whether they are inverse functions.

- AThey are not inverse functions.
- BThey are inverse functions.

**Q7: **

By sketching the graphs of and for , determine whether they are inverse functions.

- AThey are not inverse functions.
- BThey are inverse functions.

**Q8: **

By sketching the graphs of the following functions, which is the inverse of itself?

- A
- B
- C
- D

**Q9: **

Shown is the graph of . Find the intersection of the inverse function with the .

- A
- B
- C
- D
- E

**Q10: **

Find the coordinates of the intersection points of the graph of and its inverse.

- A
- B
- C
- D
- E

**Q11: **

Find the points of intersection of the graph of the inverse of and the .

- A
- B
- C
- D
- E

**Q12: **

Find the points of intersection of the graph of the inverse of and the .

- A
- B
- C
- D
- E

**Q13: **

Given the graph of , find the intersection of with its inverse function, .

- A
- B
- C
- D
- E

**Q14: **

The following is the graph of . Find the intersection of the inverse function with the .

- A
- B
- C
- D
- E

**Q15: **

What is the value of that would make an inverse of itself?

- A
- B
- C
- D1
- E2

**Q16: **

Consider the Graph of function .

Which of the following Graphs represents the inverse function ?

- A
- B
- C
- D

**Q17: **

If we drew the function and its inverse function on the same graph, which of the following must be true?

- AThere would be symmetry about the line .
- BThere would be symmetry about the .
- CThere would be symmetry about the origin.
- DThere would be symmetry about the .
- EThe two graphs would be the same.

**Q18: **

By sketching the graphs of and , determine if is the inverse of ?

- ANo
- BYes

**Q19: **

The graph of for the interval is shown. Which of the points , , and lies on the graph of its inverse function ?

- A
- B
- C

**Q20: **

The graph of is shown. Which of the points , , and lies on the graph of the inverse function ?

- A
- B
- C

**Q21: **

The graph of for is shown. Find the intersection of its inverse function, , with the .

- A
- B
- C
- D
- E

**Q22: **

The graph of the function is shown. Which of the following is the graph of the inverse function?

- A
- B
- C
- D
- E

**Q23: **

Which of the following Graphs represents a function and its inverse function ?

- AGraph 4
- BGraph 2
- CGraph 3
- DGraph 1

**Q24: **

The graph of the function is shown.

Which of the following is the graph of the inverse function ?

- A
- B
- C
- D
- E

**Q25: **

The following is the graph of the function such that . What is the value of ?

Which of the following is the graph of the inverse function?

- A
- B
- C
- D
- E