Objectives:

The student will be able to:

• Determine using composition if two functions are inverses of each other
  
• Determine if a function given as an equation is one-to-one
  
• Determine if a function given as a graph is one-to-one
• Algebraically find the inverse of a one-to-one function given as an equation
• Describe a function and its inverse as symmetric to each other over the line y = x
  
• State the domain and range of a function and it inverse
• State the relationships between the domain and range of a function and its inverse
• Restrict the domain of a function that is not one-to-one so that an inverse function can be found
• Draw the graph of the inverse function given the graph of the function
  

Examples:

• If and , find each of the following:
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• 

• Determine if each of the functions below is one-to-one:
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• 
• 
  

• Find the inverse function of .  Find the domain and range of the function and its inverse.
  

• Find the inverse function of .  Find the domain and range of the function and its inverse.
  

• Find the inverse function of .  Find the domain and range of the function and its inverse.
• Find the inverse function of .  Find the domain and range of the function and its inverse.
  

• The function  is not one-to-one.  Choose a largest possible domain containing the number 100 so that the function restricted to the domain is one-to-one.  Find the inverse function for that restricted function.

• Draw the graph of the inverse function for the graph of f(x) shown below.