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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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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

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

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)}


Ex: Graphs


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 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

  • 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


But, that’s not right…


Limits

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


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

Classwork – Worksheet 7.4 Inverse Functions

Homework – Practice Problems (25)


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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