Post date: Sep 25, 2012 11:32:51 AM
Today we continue to look at inverses of functions. We looked at how to find the inverse, what the graph of an inverse looks like compared to the original function, and when an inverse is itself a function.
Here are the marked class slides.
For the day off tomorrow (Yom Kippur on Wednesday), your homework will be two things. First complete the "Comparing Composition and Multiplication" Investigation (use your textbook to help you) and also please complete page 52, #8-28 but only the multiples of 4.
For the homework investigation, there is a typo. The very last question should read "When does a function not have an inverse?". Also, we did the first row, albeit a bit rushed, in class. Closure means that an operation on a certain kind of thing creates that same kind of thing. So, for multiplication, when we multiply two numbers, our result is still a number, so multiplication on numbers is closed. And, with functions, when you compose two functions, you still get a function, so composition on functions is also closed. An example of something that is not closed is division on the whole numbers, because if we divide 8 by 4, we'll get 2, all whole numbers, but if we divide 8 by 16, we get 0.5 which is not a whole number.
You can find the definitions of the other terms in the textbook, in case you've forgotten their meaning.