Understand
1. One of the things that I understand is how to find the inverse of functions. All you have to do is solve for y and then substitute it with f^-1(x) at the end.
Ex: f(x)= x^2
-First you would change f(x) to x and x to y although you can do it at the end. The equation would end up being x=y^2. Next, you would have to solve for y and you do that by squaring both sides so it would become y=sq. root of x. Lastly, you substitute y with f^-1(x). The inverse of f(x)= x^2 is f^-1(x)= sq. root of x
2. Another thing I learned is how to verify whether both equations are inverses of eachother. All you would have to do is solve f(f^-1(x)) and f^-1(f(x)). The results of both should be the same
-In this case they both equal to x.
3. I also learned how to prove that a function is a one-to-one. The graph of the function must pass the horizontal line test, meaning that there should not be more than one point for each horizontal line. If the graph passes this test, then it proves that the inverse of that function is a function as well.
4. Although I didn't understand logs very much, I did learn how to solve those problems a little better thanks to her little story.
Ex:log(3)81=x
-81 would remain on that side, 3 would move to the other side and x would be bumped up. The new equation ould be 3(to the power of x)=81.
From there, I would solve the problem in my hide.
Confused
I am not a big fan of logarithms simple because there are so many things you have to do to solve it and it's hard remembering all of the steps.
Ex: 2(to the power of x)-2(to the power of -x)/3= 4
-I only got up to 2(to the power of x)-2(to the power of -x) = 3 by cross multiply and I got stuck.
Also, I don't know how to graph logarithms. I rely on the calculator to do that.