B.O.B. -A Reflection

One day in Mr. Jackson's class he decided to challenge the class by making us have to create a composition function and find the final domain of it.  Originally I was really confused and I accidentally made it the wrong way around by trying to simplify something that I couldn't get any simpler.  But my group noticed and pointed it out to me explaining why I couldn't do it that way.  Then I had to find the domain, so I took all three domains from the f(x) the g(x) and the f(g(x)) creating one very large union.  I noticed how large it was and thought that it couldn't be true and so I checked the problems on my calculator.  I found out that I was right about the domain being wrong so I went back to the paper explaining how to find the domain of a composition function.  It said that you had to add the domain of the combined function to the domain of the inner function to get the domain of the combined function.  This confused my group for a few minutes because we were thinking that you needed the answer to find the answer.  Thus I realized we had been thinking of it in the wrong way, there are actually two domains for the final combined function, a first domain and a final domain being the answer.  I explained this to my group and it helped us a lot and we were able to shrink down our original domain considerably, and finding the correct answer to the problem.  After that the next few problems Mr. Jackson have us were quite easy.  But every now and then a person in the group would get confused (even me), and we would all look at what they had done and we would help them with their mistake.  Thanks to being in the group we all were able to check and compare our answers thus allowing us to figure out how to do those problems on our own witch will allow us to remember it better because we came up with it instead of just being told how to do it that way.  Working in groups that day was a lot of fun and it definitely helped us all remember the information from that day.