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Manipulating Radical Functions

Manipulating Radical Functions 1.7 - Solution

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We want to determine whether the given pair of functions are inverse functions. To do so, we need to verify that the compositions of and are the identity function.

To find the expression for we will start by substituting for We will now apply the definition of Finally, let's simplify and see if the function is the identity function.
We found that is the identity function.

We will now investigate the expression To find the expression, this time we will start by substituting for Now, we will apply the definition of Finally, let's simplify and see if the function is the identity function.
We found that is also the identity function. Therefore, and are inverse functions.