Findng Inverses of Formulas and Compositions of Inverse Functions

In this video math lesson, working with inverse functions is discussed. It is good to remember, when finding the the inverse of a formula, DO NOT SWITCH THE VARIABLES. The first example models finding the inverse of an existing formula:
d = 16t^2
16t^2 = d Symmetric Property of Equality
t^2 = \frac{d}{16} Division Property of Equality
\sqrt {t^2} = \sqrt{ \frac{d}{16}} Inverse of Square is Square Root
t^ = \frac{ \sqrt{d}}{4} Simplify Fraction to Simplest Radical Form

I know some readers may not be able to follow the above problem. The same problem, but with the example in the video, the auditory learner can benefit too.

The second example models finding the composition of a function and its inverse. This can be written as f^{-1}(f(x)) or f(f^{-1}(x)). In both cases are equal to the value of x. Performing the composition of a function and its inverse gives the value you started with. You will see in the video, how simple this process is.

If you have a question or this video helped you, leave a comment.


2 Responses

  1. How did you get from 652 to -square root of 86?

    • Jack,

      In the last example, I there are really two examples being worked out. The example was illistrating the fact if you take the composition of a function and its inverse, then the answer you get is what you started with.

      Kind Regards,

      Mr. Pi

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