Verify 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.

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