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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.

Find the Domain of a Function and Its Inverse

In this post, I have embedded an Algebra 2 Video Math Lesson about the function $f(x) = \sqrt {2x+2}$. Before considering the function, the video defines $f^{-1}$ as the inverse of f or as f inverse.

The video models how to:

1. Find the domain and range of $f(x) = \sqrt {2x+2}$
2. Find $f^{-1}$
3. Find the domain and range of $f^{-1}$
4. Determine if $f^{-1}$ is a function

If you have any questions regarding the video lesson or other questions regarding finding the inverse of a function, use the comments section.

How To Find and Graph the Inverse of a Function

In this video Algebra 2 Math Lesson, I model how to graph a quadratic function and its inverse. The process starts with graphing a parabola in the form $y=a^2+c$. The vertex is given by (0,c). After graphing the parabola with four additional points, I create the inverse’s graph by moving the points about y = x line. Finally, I find the inverse of the original function.

If this video math lesson on finding the inverse of a function and then graphing it helped you, leave a comment. Heck, if it didn’t help leave a comment and let me know how to make it better.

How to Find the Inverse of a Relation and an Equation

This video lesson covers the definition of the inverse of a relation and reviews the concept of how to find the inverse of a relation.

Example 1 covers how to find the inverse of a relation from a table of values and provides a good visual of a relation that is a function and its inverse is not a function.

Before example 2, a discussion about how switching the x and the y in the equation is the best method for finding the inverse of a function. Example 2 models how to use the x and y switcheroo to find the inverse of a given function.