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Verify Inverse Functions




 

Videos and lessons to help High School students learn how to find inverse functions.

B. Verify by composition that one function is the inverse of another.
Common Core: HSF-BF.B.4

Related Topics:
Common Core (Functions)

Common Core for Mathematics

Ex 1: Determine If Two Functions Are Inverses

This video provides two examples of determine if two given functions are inverses of one another by using composition of functions.

Ex 2: Determine If Two Functions Are Inverses

This video provides two examples of determine if two given functions are inverses of one another by using composition of functions.



Verifying that Two Functions are Inverses of Each Other

This video describes how to verify that two functions are inverses of each other using composition of functions.

Wolfram Inverse Composition Rule

If f(x) is the inverse function of g(x), then f(g(x)) = g(f(x)) = x . In this Demonstration you can choose two functions f and g. The graphs of f and g are drawn with red and blue dashes. Choose the composition f(g(x)) or g(f(x)). The graph of the composition is drawn as a solid green curve. If it is the line y = x , the functions are inverses of each other. If the solid curve is only partly the same as the line y = x , the domain of the functions has to be restricted.




 

Verifying Inverse Functions

For every function, there is an inverse function. For every inverse function, there is a function. In order to verify this algebraically, one must substitute f(x) into f-1(x) and then f-1(x) into f(x). If this results in both expressions equaling x, then the functions are inverses of one another.

Prove inverse functions

Prove f(x) and g(x) are inverse functions.


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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