I know some of you are behind. I do expect my students to do the work daily even though I don’t collect the work daily. Make sure you are working hard in class. It makes your work outside of class easier. We meet for about 4.5 hours a week. Time in class is precious. Make sure you are focused and on-task in class.
If you cannot state the domain of power functions then you are behind. Look at these notes.
Today you will be looking at inverse functions of power functions. It builds upon your work from last time, where you looked at inverse functions of linear functions. Remember the 3 steps needed to find an inverse function (they are listed at the top of Inverse Functions Exploration 1). Remember about the “switch x and y” idea… and how it shows up in the table and on the graph. And remember your result for function composition.
If f and g are inverse functions, then
f(g(x))=x and g(f(x))=x
You will first find inverse functions of power functions. Remember your exponent rules. Next, I will give you some points on the graph of f. Know, knowing what you know about inverse functions, can you state some points on the graph of g? Then algebraically verify the points are on the graph of g. Just substitute the x value into the function and make sure the output (y-value) is what you expect.
If (x,y) is on a graph, then g(x)=y
For instance, if I have a point (12,2) on a graph, then g(12)=2.
Then you get to show that f(g(x))=x and g(f(x))=x. Show all steps. Yes, we know what the result is supposed to be (if you found g correctly). So make sure you can show it algebraically.
And here are the solutions to the first page. You have 3 pages to do on your own.
A reminder… I routinely tell people that I get to teach the best kids in the school. Today you get to show that. I have high expectations. Please meet them. Thank you.