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.


6 Responses

  1. What do you think about teaching inverses of functions to middle schoolers in general without having to use visuals? Using pure algebraic terms with simple equations, I think it works out well, but this doesn’t seem to be a popular topic in almost any curriculum I’ve seen.

    • I am not sure about teaching middle schoolers inverses of functions without any type of visual or hands on option. Jesse, I think there many variables that would determine if a middle school student could handle leaning about inverses in a purely algebraic manner. I am interested in finding out more about your experiences with this topic with such a young age group.

  2. Hey thanks for responding! I try to relate it to how they already understand that operations have inverses (addition-subtraction, multiplication-division), just to get the idea in their heads of what they’re doing when they are finding the inverse of a function.

    My first post was probably a little unclear in this regard, but I didn’t mean without visuals entirely in terms of an entire curriculum. Looking at the graphs of simple functions and their inverses and how they are symmetric around y = x is a must, I feel.

    • No problem for the reply! Hey thanks for the comment.

      I think that teaching inverses in middle school should be left at ordered pairs on and off of the coordinate plane. Maybe extend it linear function, but that should start after learning about inverse of relations as a set of ordered pairs.

      It could even be used as an extension to a lesson for the more advanced students in a middle school math class.

  3. Hi again,

    I mostly work with home school kids in the area in small groups of 3-5. What originally got me wondering about this was that I tried this one idea using fruit on a whim and it seemed to have worked well, and I showed a linear equation that represented what we were talking about with the fruit, and it seemed to click.

    There was a bag of small oranges (maybe tangerines?) in the living room we were working in, and I had a small whiteboard sat up. I gave the kids the idea of a function on the oranges where we would, for example, double however many oranges we started with and then add three. We did a few examples of this where they each got to work out a problem individually, and then showed them the linear equations that represented what they were doing. After we graphed them, then we looked at the idea of an inverse on these linear functions, and that seemed to really get them to think and be engaged and understand what an inverse really meant in terms of “undoing” a function.

    Sorry for the wall of text lol.

    Best Wishes,

    • Wow Jesse!! That was an awesome idea with the fruit. I am sure I will use a similar idea when working with inverses at the Algebra 1 and Algebra 2 levels in the coming school year.

      Don’t worry about the wall of text, this is the type of interaction I was hoping for when I started this blog.

      Here is the link for my teaching blog:

      I just started to really add content this past week.

      Kind Regards,

      Mr. Pi

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