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Inverse Functions

A series of free Intermediate Algebra Video Lessons from Brightstorm online Algebra series.

Definition of One-to-One Functions
After learning the definition of a function, we can extend it to define a one to one function. A one to one function has not only one output for every input, but also only one input in the domain for every output in the range. Another interesting type is an invertible function, or a function that has an inverse. The graph of a one to one or invertible function has unique and interesting characteristics.

Definition of Inverse
The definition of a function can be extended to define the definition of inverse of a function. Along with one to one functions, invertible functions are an important type of function. The definition of inverse says that a function's inverse switches its domain and range. The definition of inverse helps students to understand the unique characteristics of the graphs of invertible functions.

Finding an Inverse Algebraically
Once we learn the definition of a function's inverse we learn how to find the algebraic inverse, or how to find the inverse using algebraic methods. There are different methods for finding the inverse, the most common of which is to switch the dependent and independent variables and solve for the dependent variable. This is an important step in learning how to prove the inverse of a function.

Proving Two Functions are Inverses
The definition of a function can be extended to define the definition of an inverse, or an invertible function. It's important to understand proving inverse functions, and the method of proving inverse functions helps students to better understand how to find inverse functions. Students should review how to find an inverse algebraically and the basics of proofs.

Finding an Inverse Graphically
In order to understand graphing inverse functions, students should review the definition of inverse functions, how to find the inverse algebraically and how to prove inverse functions. The graphs of inverse functions and invertible functions have unique characteristics that involve domain and range. Techniques for graphing inverse functions can make it easier to graph certain functions by hand.

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