# 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 