Hi everyone! Read through the material below, watch the videos, and follow up with your instructor if you have questions.
Lesson 7: The inverse of a function
Topic. This lesson covers Session 7: The inverse of a function
- Identify one-to-one functions and understand the connection to inverse functions.
- Form connections between the definition of inverse functions, the notation of inverse functions, and the application of inverse functions.
- Find the inverse of a function graphically and algebraically.
WeBWorK. There is one WeBWorK assignment on today’s material:
- Functions – Inverse Functions
Additional Video Resources.
Question of the Day: What is the opposite of ?
Definition. A function is called one-to-one (or injective), if two different inputs always have different outputs .
Example. Consider the functions and , shown in the diagram below. Are either of these functions one-to-one?
Observation (Horizontal Line Test). A function is one-to-one exactly when every horizontal line intersects the graph of the function at most once.
A function is one-to-one when each output is determined by exactly one input. Therefore we can construct a new function, called the inverse function, where we reverse the roles of inputs and outputs.
Definition 7.5. Let be a function with domain and range and assume that is one-to-one. The inverse of is a function so that
Example. Find the inverse of each function:
VIDEO: Finding the Inverse of a Function
Video by Irania Vazquez
Good job! You are now ready to practice on your own – give the WeBWorK assignment a try. If you get stuck, try using the “Ask for Help” button to ask a question on the Q&A site.