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Common Core Standard: HSF.BF.4

Inverse Functions and Composite Functions

Overview of the Unit:

Description of the video and note-taking guides:

Lesson 1 
Properties of exponents

  • This lesson reviews rules of exponents with the operations of adding, subtracting, multiplying and dividing terms with exponents. 

  • It also covers handling negative exponents.  

  • Mastering the exponent rules is essential for later lessons.

Lesson 2 Function Operations 

  • This lesson covers adding, subtracting, multiplying and dividing functions.  
  • Limits on the domain for the division problems are addressed. 
  •  Many different examples of dividing,adding,subtracting and multiplying functions are presented.
Lesson 3 Composition of Functions 

  • This lesson teaches students to evaluate single functions and composite functions two different ways.
  • Students learn how to write composite functions and simply them. 
  • Multiple examples are presented.
Lesson 5  Finding the Inverse Function

  • Lesson 5 defines and teaches student how to find the inverse of a function algebraically.  
  • Step by step directions are given. 
  •  Examples included are linear, quadratic and cubic.
​Lesson 6 Verifying Inverse Functions

  • This lesson teaches student how to verify if two functions are inverses using composition of functions.  
  • To verify, f(x) and g(x) are inverses, find f(g(x)) and g(f(x)). 
  •  They should both simple to x.  
  • Basic concepts of graphing inverses are presented, ex. (2,3) and (3, 2) are inverses.  
  • Discussion of the domain and range and how inverses switch x and y coordinates. Functions vs. relations are discussed.
Lesson 7 Inverse Functions and Graphs

  • One to one is defined.  
  • Vertical and Horizontal line tests using the one-to-one concept are taught.  
  • Graphing inverse functions for a line, a quadratic and a cubic are taught using the y=x line and switching the domain and range values.

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Summary of Composition and Inverse of Functions Unit concepts: This unit coveres evaluating functions, both single functions and composite, as well as simplifying composite functions, i.e. f(g(x)). The four operations with functions with functions, adding, subtracting, multiplying and dividing, are explained. Limits on the domain are discussed with rational composite functions. Students are taught inverse function, both algebraically and graphically.