1 / 13

Understanding Inverse Functions: Concepts and Methods Explained

Dive into the fundamentals of inverse functions in mathematics with this comprehensive guide. Learn about the key principles, including the rule for reflection over the line y = x and how to find inverse functions both graphically and algebraically. We’ll explore function notation, switching x and y values, and the impact of limited ranges on domain. Practice problems are provided to reinforce your understanding, along with classwork and exit ticket discussions to enhance learning. Discover how to determine the inverse function effectively!

liza
Télécharger la présentation

Understanding Inverse Functions: Concepts and Methods Explained

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Bell Ringer What do you think “inverse” means? What is the rule for reflection over the line y = x? Find the “sin” button on your calculator. What is written above it?

  2. Inverse Functions Thursday, March 13, 2014

  3. The Basics The inverse of a function is when you switch the x and y values. The graph of inverse functions is a reflection over the line y = x. Inverse function notation is f -1(x).

  4. Ex: Switching x and y Find the inverse of the given function: f = {(1,2), (3,5), (-2,-5), (-7, 4)} The inverse is: f -1 = {(2,1), (5,3), (-5,-2), (4, -7)}

  5. Ex: Graphs

  6. Finding the Inverse Algebraically (See Graphic Organizer) Switch to the y = notation from the f(x) =. Exchange x and y in the problem and solve for y. Rewrite as f -1(x).

  7. Ex: Solving Algebraicallyf(x) = 3x2 - 8 • Switch notation • Switch x & y and solve for y • Add 8 to both sides • Divide both sides by 3 • Take the square root • Rewrite in function notation • y = 3x2 – 8 • x = 3y2 – 8 • x + 8 = 3y2 • x + 8 = y2 3 √ (x + 8) = y 3 f -1(x) = ± √ (x + 8) 3

  8. Ex: Solving Algebraically • f(x) = √x • y = √x • x = √y • x2 = y • f -1 (x) = x2 • Copy • Rewrite in y = form • Switch x and y & solve for y • Square both sides • Write in function notation

  9. But, that’s not right…

  10. Limits If a function has a limited range, then the domain of its inverse is limited.

  11. Ex: Limits f(x) = √x The range of this function is y ≥ 0 This means the inverse function has a limited domain of x ≥ 0 So, f -1(x) = x2, x ≥ 0

  12. Practice Problems Classwork – Worksheet 7.4 Inverse Functions Homework – Practice Problems (25)

  13. Exit Ticket What are the 3 ways to determine the inverse of a function? Which way do you find easiest? Explain.

More Related