Inverse Functions
Overview
You already know how a function turns an input into an output. An inverse function does the reverse: it takes the output back to the input it came from. Think of it as the undo button for a function. If one machine doubles a number and adds three, the inverse machine must subtract three and then halve, exactly reversing each step in the opposite order.
But not every function can be undone. In this lesson you will learn the crucial test of whether an inverse even exists, why a function must be one-one to have one, and the reliable swap-and-rearrange method for finding the inverse. These ideas sit at the heart of the Functions section and reward careful, tidy algebra.
Objectives
- Explain in words why a given function does not have an inverse.
- Find the inverse of a one-one function and use correct notation.
Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Inverse Functions. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- What is the inverse of f(x) = 2x + 3? A. (x - 3)/2 B. (x + 3)/2 C. 2x - 3 D. 1/(2x + 3) Answer: A
- Which type of function always has an inverse? A. Many-one B. One-one C. Quadratic over all reals D. Constant Answer: B
- Why does g(x) = x^2 (for all real x) have no inverse? A. It is undefined at 0 B. It is one-one C. It is many-one, since 2 and -2 both give 4 D. It has no range Answer: C
- The inverse of f(x) = x/4 - 5 is: A. 4x - 5 B. 4(x + 5) C. (x - 5)/4 D. 1/(x/4 - 5) Answer: B
- If f(4) = 11, what is f^{-1}(11)? A. 11 B. 1/11 C. 4 D. 7 Answer: C
Available on the Green Bridge App
Download the Green Bridge CBT app on your phone or computer to access full lesson notes, practice questions, and more.
Available on the Green Bridge App
Download the Green Bridge CBT app on your phone or computer to access full lesson notes, practice questions, and more.
Recommended Books
Practice Mock Questions
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