Topics:
• More on composition of functions (Example 6.8 (a) and (c)) and finding domains of composite functions
• Operating on functions using a table (Example 6.9) – we will see more functions using tables next time as well
• One-to-one functions
• Inverse functions: definition; how to find the formula for an inverse of a function, graphs of inverse functions, and the “Round-trip” theorem to check if two functions are inverse to each other. [Link to Cool Math]
Examples: 7.6 (finding the formula, domain and range of inverse functions)
The notes and graph I handed out in class are also available here:
The graph comes from the website “Cool Math” and it is a good idea to read through what they have to say about inverse functions!
If a function is not one-to-one, then we will have to restrict to a part of its domain where it is one-to-one before we can find an inverse function. The “Cool Math” website shows why this is so. We used this in Example 7.6(e)
Here are some good videos from Patrick’s Just Math Tutorials:
Finding the inverse of a function [Example 1]
Finding the inverse of a function or showing the inverse does not exist [Example 2]
Finding the inverse of a function or showing the inverse does not exist [Example 3]
Finding the inverse of a function or showing the inverse does not exist [Example 4]
Homework:
• Review the examples we discussed in class. Make sure that you look to see how the inverse function is “undoing” what the original function does to the variable x.
• Important: there are problems in the textbook that are not included in the WeBWorK. Make sure that you do these as well as the WeBWorK!
In Session 6: do Exercise 6.6
In Session 7: do Exercise 7.2 (a-f and l-p) and 7.4 (a-c). In Exercise 7.4, you are to check whether or not the functions are inverses by using the “Round-trip” theorem (Observation 7.9 in the textbook). Also do Exercise 7.5 (a).
• Do the WeBWorK, which is not due until next week, but please do not wait to the last minute! Try to do at least some of it by Wednesday’s class
• There will be a quiz next time, on the topics of even and odd functions (from last time) and composition of functions
Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question. And please only put one problem per posted question!
