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Bell Ringer

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? . Inverse Functions. Thursday, March 13, 2014. The Basics.

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Bell Ringer

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  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.

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