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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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Presentation Transcript
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

Inverse Functions

Thursday, March 13, 2014

the basics
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).

ex switching x and y
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)}

finding the inverse algebraically
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).

ex solving algebraically f x 3x 2 8
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

ex solving algebraically
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
limits
Limits

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

ex limits
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

practice problems
Practice Problems

Classwork – Worksheet 7.4 Inverse Functions

Homework – Practice Problems (25)

exit ticket
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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