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 𝑓(𝑥)=2𝑥−1.

Which one is the graph of the inverse function 𝑓(𝑥)?

  • A(b)
  • B(a)
  • C(c)

Q2:

Consider the two following figures.

The first figure shows the graph of 𝑓(𝑥)=𝑥 and a tangent to the graph with gradient 1. This tangent meets the graph at a point with 𝑥-coordinate 1√3.

The second figure shows the graphs of 𝑔(𝑥)=𝑥+𝑏 and its inverse 𝑔(𝑥)=(𝑥−𝑏). The graphs cross in the third quadrant and touch in the first quadrant.

What is the value of 𝑏?

  • A𝑏=−4√39
  • B𝑏=−2√39
  • C𝑏=4√39
  • D𝑏=2√39
  • E𝑏=−1√3

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

  • A√3 and −1√3
  • B1√3 and −2√3
  • C√3 and −5√3
  • D1√3 and −√39
  • E1√3 and −5√3

Q3:

The graphs of 𝑓(𝑥)=𝑥+𝑏 and its inverse 𝑓(𝑥) intersect at three points, one of which is 45,45.

Determine the value of 𝑏.

  • A64125
  • B45
  • C36125
  • D164125
  • E−45

Find the 𝑥-coordinate of the point 𝐴 marked on the figure.

  • A45
  • B164125
  • C−45
  • D36125
  • E64125

Find the 𝑥-coordinate of the point 𝐵 marked on the figure.

  • A−2−√135
  • B825
  • C36125
  • D13
  • E√13−25

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 𝑓(𝑥). Do the blue points represent 𝑓(𝑥)?

  • ANo
  • BYes

Q6:

By sketching the graphs of 𝑓(𝑥)=3𝑥−1 and 𝑔(𝑥)=√𝑥+13 for 𝑥≥0, determine whether they are inverse functions.

  • AThey are not inverse functions.
  • BThey are inverse functions.

Q7:

By sketching the graphs of 𝑓(𝑥)=2𝑥 and 𝑔(𝑥)=𝑥2 for 𝑥≥0, 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?

  • A1𝑥
  • B𝑥
  • C𝑥
  • D1𝑥

Q9:

Shown is the graph of 𝑓(𝑥)=5𝑥+6. Find the intersection of the inverse function 𝑓(𝑥) with the 𝑥-axis.

  • A−65,0
  • B56,0
  • C(−6,0)
  • D65,0
  • E(6,0)

Q10:

Find the coordinates of the intersection points of the graph of 𝑓(𝑥)=3𝑥+4 and its inverse.

  • A−43,0
  • B(0,4)
  • C0,−43
  • D(4,0)
  • E(−2,−2)

Q11:

Find the points of intersection of the graph of the inverse of 𝑓(𝑥)=𝑥+3 and the 𝑦-axis.

  • A(0,3)
  • B(3,0)
  • C(0,1)
  • D(0,−3)
  • E(−3,0)

Q12:

Find the points of intersection of the graph of the inverse of 𝑓(𝑥)=2𝑥+3 and the 𝑥-axis.

  • A0,−32
  • B−32,0
  • C(0,3)
  • D(−3,−3)
  • E(3,0)

Q13:

Given the graph of 𝑓(𝑥)=3𝑥+2, find the intersection of 𝑓(𝑥) with its inverse function, 𝑓(𝑥).

  • A−12,1
  • B−1,12
  • C−1,−12
  • D−12,−1
  • E(−1,−1)

Q14:

The following is the graph of 𝑓(𝑥)=(𝑥−3)−1. Find the intersection of the inverse function 𝑓(𝑥) with the 𝑦-axis.

  • A(0,8)
  • B(0,−4)
  • C(0,2)
  • D(0,4)
  • E(0,−2)

Q15:

What is the value of 𝑎 that would make 𝑓(𝑥)=−𝑎𝑥−2 an inverse of itself?

  • A−2
  • B12
  • C−1
  • D1
  • E2

Q16:

Consider the Graph of function 𝑓(𝑥)=1−2𝑥.

Which of the following Graphs represents the inverse function 𝑓(𝑥)?

  • AGraph1
  • BGraph4
  • CGraph2
  • DGraph3

Q17:

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

  • AThere would be symmetry about the line 𝑦=𝑥.
  • BThere would be symmetry about the 𝑥-axis.
  • CThere would be symmetry about the origin.
  • DThere would be symmetry about the 𝑦-axis.
  • EThe two graphs would be the same.

Q18:

By sketching the graphs of 𝑓(𝑥)=2𝑥+1 and 𝑔(𝑥)=𝑥−12, determine if 𝑔(𝑥) is the inverse of 𝑓(𝑥)?

  • ANo
  • BYes

Q19:

The graph of 𝑓(𝑥)=(𝑥−2)+3 for the interval [2,∞) is shown. Which of the points 𝐴(3,1), 𝐵(7,4), and 𝐶(9,5) lies on the graph of its inverse function 𝑓(𝑥)?

  • A𝐵
  • B𝐴
  • C𝐶

Q20:

The graph of 𝑓(𝑥)=4𝑥−7 is shown. Which of the points 𝐴(2,3), 𝐵(−2,2), and 𝐶(1,2) lies on the graph of the inverse function 𝑓(𝑥)?

  • A𝐵
  • B𝐶
  • C𝐴

Q21:

The graph of 𝑓(𝑥)=𝑥+2 for 𝑥=[0,∞] is shown. Find the intersection of its inverse function, 𝑓(𝑥), with the 𝑥-axis.

  • A(1,0)
  • B(4,0)
  • C(−2,0)
  • D(2,0)
  • E(−1,0)

Q22:

The graph of the function 𝑓(𝑥)=𝑥+2 𝑥≤0 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 𝑓(𝑥) and its inverse function 𝑓(𝑥)?

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

Q24:

The graph of the function 𝑓(𝑥)=𝑥+1 is shown.

Which of the following is the graph of the inverse function 𝑓(𝑥)?

  • A
  • B
  • C
  • D
  • E

Q25:

The following is the graph of the function 𝑓(𝑥)=𝑥+𝑎𝑥 such that 𝑥≥−1. What is the value of 𝑎?

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

  • A
  • B
  • C
  • D
  • E

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