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

Verify by composition that one function is the inverse of another.

**Common Core: HSF-BF.B.4**

### 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.

Inverse Composition Rule from the Wolfram Demonstrations Project by Ed Pegg Jr

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