## Thursday, April 16, 2009

### Writing Inverse Functions

I like Sam Shah’s approach to teaching function inversion. It’s pretty much what I had intended to do this year, but somehow forgot about at some point. Hopefully writing these notes here will increase the odds that I get it right next time around. The original inspiration was Mr. K’s approach to solving two-step equations, and the following will make no sense without having read that entry, so do that first.

I showed my Algebra 2 students Mr. K’s series of boxes and arrows for solving equations early in the year, and they thought it was fun. We did more complicated cases such as 5-3(x+5)=2 and -2-(2x+3)=-5. It was great for reviewing Order of Operations in a novel way. Many students had started out subtracting 3 from 5 in the fist equation, and in the second case very few students were able to identify “multiply by -1” as one of the operations in the sequence. However, after working through a few cases they got quite fluent at writing sequences of operations such as for the equation -2-(2x+3)=-5, where the operations on x are:
1. Multiply by 2