At the start of class we of course reviewed the previous day's homework, which was section 8.2. After our homework review we wet over Mikaela's last post on section 8.2. This took up a good chunk of time. Mr. Cope also talked about how he takes things personally when he doesnt need to. Like when a student falls asleep in his class, it's not his fault. The student definetly should have went to sleep earlier and possibly slept in the previous class so that it didn't happen in Mr. Cope's. We then talked about how Mr. Cope and how he hasn't caught anyone texting during class in a while.
Section 8.3 is about the properties of inverse functions. Here's the basic objective you need to know before you start computing anything:
1. We denote the inverse of a function as f^-1. (f^-1 means the inverse of a function)
2. For every point (a,b) on the graph of f, the point (b,a) is on the inverse graph. (the point (a,b)'s inverse is (b,a))
3. To determine whether the inverse is a function or not without graphing, we apply the horizontal line test. (use the h.l.t. to see if the inverse will be a function without graphing)
Given the general equations y=x, y=x^2, and y=x^3, we know that y=x is a function using h.l.t., y=x^2 is not a function because it doesn't pass h.l.t., and y=x^3 is a function because it passes h.l.t.
The three steps to finding an inverse are...
1. Replacing f(x) with y
2. Switching x and y
3. Solve for y
When combining any two functions the inverse "undo" eachother. For example when we plugged g(f(x)) and f(g(x)) into the calculator both outcomes equaled x.
On a test Mr. Cope may say are these two functions inverses? To solve this you would simply plug the functions into eachother [g(f(x)) and f(g(x))].
The inverse function theorem states that two functions if and only if f(g(x))=x and g(f(x))=x.
The tricky part was power functionsand inverses.
f(x)=x^6's inverse wouldn't be a function because it's a parabola. Parabolas never ever pass h.l.t. It causes a problem when you attempt to plug negative numbers into the inverse function. X can't be negative in an inverse. So to take care of that you can restrict the domain to X is greater than or equal to 0.
f(x)=x^an odd number passes h.l.t., and is much simpler than an even power function.
Next blogger is... Emma B!