## Reflection: Developing a Conceptual Understanding Finding the Inverse of a Function Day 1 of 2 - Section 2: Discovering the definition of inverse functions

I taught this lesson during the block day or our weekly schedule. We have one day a week that the class meets for approximately 90 minutes. This means that I have  2 of my classes one day and then the 3rd class the next day.

During the first day of instruction I noticed the student were saying that 2 functions were inverses when f(g(x))=g(f(x)). They did not understand that the result would always give the original domain value. After seeing this in the first class I started thinking about how I could fix this misconception. The same confusion came up in the second class. At this point I had the students evaluate the compositions for x=2. The students saw how the answer came out 2 so they added x.

After thinking more about this issue I decided that the students probably did not really understand that the answer will always come out with the domain value. I decided to expand on the adjustment for the last class. For this class I gave each group a different domain value. The students worked and then shared their answers.

As students worked I heard one comment that the definition said the answer will be x so that means it should be 2 since we were given x=2. Do both answers come out as 2? This was great problem solving and understanding for that group.

I also have a group of students whose algebra skills are weak. I gave this group x=0 so that they could complete the problem quickly. Even with this the group found the 2 answers were not equal. The other groups helped the students find the algebra mistake and corrected their answers.

I plan to use this new idea next year to make sure students really understand the definition of inverses.

Developing a Conceptual Understanding: Adjustment in instruction

# Finding the Inverse of a Function Day 1 of 2

Unit 2: Functions and Piecewise Functions
Lesson 10 of 15

## Big Idea: By reading and discussing a mathematical text, a process for finding inverses will be uncovered.

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55 minutes

### Katharine Sparks

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