Lesson: Graphs of Inverses of Functions Mathematics

In this lesson, we will learn how to use a graph to find the inverse of a function and analyze the graphs for the inverse of a function.

Lesson Plan

Students will be able to

  • understand that the graph of a function and the graph of its inverse are reflections in the line 𝑦=𝑥,
  • identify the graph of the inverse of a function when given the function graph,
  • sketch the graph of the inverse of a function when given a function graph,
  • identify whether the inverse of a function is itself a function,
  • find the points of intersection of the graph of the inverse of a function and the 𝑥-axis or 𝑦-axis,
  • find the coordinates of the intersection points of the graph of a function and its inverse.

Lesson Presentation

Lesson Video

Video Thumbnail
16:01

Lesson Explainer

Lesson Worksheet

Q1:

The following is the graph of 𝑓(𝑥)=2𝑥−1.

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?

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

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.

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

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

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