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Finding Inverses of Functions

Finding Inverses of Functions

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Author: Stephanie Nazario
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Tutorial

Standard: CCSS.MATH.CONTENT.HSF.BF.B.4.A

Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.

Source: Common Core State Standards Initiative - Mathematics - Functions

Objectives:

Students will be able to identify which variables to switch in order to find the inverse.

Students will be able to perform the GEMDAS Operations on a function in order to find the inverse. 

Students will be able to solve for the inverse using proper mathematics terminology.

Students will be able to write an expression for a simple inverse given in the form f to the power of negative 1 end exponent left parenthesis x right parenthesis space equals space c


PEMDAS Review!

A quick, catchy PEMDAS review to get the brain flowing!

Source: Mr.Stallings. (2012, May 31). The PEMDAS Song Remix. Retrieved July 27, 2016, from https://www.youtube.com/watch?annotation_id=annotation_494975

How to find inverse functions

Step 1:  Replace f(x) with y.

Step 2:  Switch x and y variables.

Step 3:  Solve for y using GEMDAS operations. 

Step 4: Switch y with  f to the power of negative 1 end exponent left parenthesis x right parenthesis

Watch these next three videos and think of the following....

What steps did the tutor take?

How did the teacher perform GEMDAS? What came first? Second?

Source: Clark, P., Dr. (2011, September 22). Finding Inverses (Linear). Retrieved July 27, 2016, from https://www.youtube.com/watch?v=LGgh1qPw4Mc

Step by step Guided Practice

Have your notebooks out and pencils ready.  The next one we will go over together!  Here we go!

Source: How to Find the Inverse of a Function. (2016). Retrieved July 27, 2016, from http://www.coolmath.com/algebra/16-inverse-functions/05-how-to-find-the-inverse-of-a-function-03

Make sure to pay attention and takes notes if needed.
You WILL be quizzed on this material!

Source: Schmidt, L. (2010, July 07). Graph Inverses of Linear Functions. Retrieved July 27, 2016, from https://www.youtube.com/watch?v=937JRksAJ48

Lesson Review:

Only watch up to 3:12, as there is an error in the video after that. We will discuss said error in class. Once finished, please scroll up and take the "Quiz" before completing "The Big Question" below.

Source: Pederson, C. (2015, November 03). Finding the inverse of a linear function and graphing it. Retrieved July 27, 2016, from https://www.youtube.com/watch?v=q1BbQ02C0tA

The Big Question:

On a separate sheet of binder paper, you will answer the following questions and turn them in.  These questions have the same value as a Chapter Test.  Partial credit will be awarded.  All questions need full sentences, roughly 1 to 2 sentences per question, use your best judgement.   


1.)   What steps are necessary in order to "find the inverse of a function"?

2.)   What Mathematical Vocabulary must you know in order to solve for an inverse of a function?  (List out all mathematical words necessary, no definitions needed).

3.)   In your opinion, why do we "flip" x and y in the second step of finding the inverse of a function?

4.)   Why is it necessary to know PEMDAS/GEMDAS prior to learning how to find an inverse of a function?

5.)   How did you like this lesson?  What did you learn from it?  (Honest opinion please, minimum of two "I learned" statements)


Extra Credit:

6.)   What is your teacher's favorite color? (Hint: The Ocean is wonderful!)

Disclaimer:

Portions of these materials have been incorporated under the Fair Use Guidelines and are restricted from further use.