1.1 Inverse Functions

In this lesson, you will learn about inverse functions.

Lesson Objectives

• • Review (from Precalculus) and apply symbolic and graphical properties of inverse functions.

  • Recognize that a given function has a unique inverse function if the given function is one-to-one.

  • Derive the formula for the derivative of an inverse function.

Lesson Content

View all of the following instructional videos. These will help you master the objectives for this module.

• 1. YouTube video: Inverse Functions - The Basics!

• 1. YouTube video: One to one functions (defining a one to one function)

• 1. YouTube video: Inverse of a Function (finding the inverse of a function)

• 1. YouTube video: Inverse Functions (finding the inverse of a one to one function)

• 1. YouTube video: Derivative of an Inverse Function (general formula for the derivative of an inverse function) up to example 1

• 1. YouTube video: Find the Derivative of an Inverse Function

Lesson Readings

The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.

• 1. Inverse Functions

  2. Inverse Functions

  3. Inverse Functions (basic definition, properties of inverse functions, procedure for determining the equation for f^-1 from the equation of f, the calculus of inverse function, practice exercises with solution

  4. Derivative of Inverse Functions

Lesson Practice Exercises/Activities

Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.

• 1. Inverses of Functions

  2. Inverse Functions

  3. Derivatives of Inverse Functions

Additional Resources

Below are additional resources that help reinforce the content for this module.

• 1. YouTube video: Introduction to Function Inverses

• 1. YouTube videos: Function Inverse Example 1:

• 1. Example 2:

• 1. Example 3:

• 1. YouTube videos: Finding the Inverse of a Function or Showing One Does not Exit

  2. Example 2:

• 1. Example 3:

• 1. Example 4: