1. Well First i learned that when a function is one-to-one it means the function and its inverse are both functions as in for every input(x) there is only one output(y). To check if the function one-to-one you don't need to plug in every number you can just do the vertical line test for the function and to see if its inverse is also a function you can do the horizontal line test on the same function not its inverse. (Hopefully this is clear, although i doubt it)
2. Another thing that i learned was how to find a function's inverse. It is similar to finding x in an equation such as y = 3x + 4 except the functions we are dealing with now have logs and exponents.
3. I also learned how to know if the the inverse is actually the inverse of its function. Its pretty simple. To know if the inverse is its functions' inverse all you have to do is find f(f^-1(x)) and f^-1(f(x)) and the answer for both equations should be x , but it can become one BIG, UGLY looking equation.
4. I really like the story Ms. Hwang told us about the man out in the woods in his log cabin with the gate (=) and the wild animals (#). This story helped me with converting log equations into a more common and simply looking equation
For example
from ........ log x 25 = 2 .......... to ....... 25= X^2 .... then it's easier to solve x=5
I DON'T UNDERSTAND:
One thing i didn't understand was how to solve for a functions such as:
e^x + e ^-x = 3
I tried solving it so many time and nothing. I was frustrated with this simple looking equation. I tried different way to solve it but i know somehow i was breaking a rule or making it more complex.
Im not sure if i can explain it to u correctly but somehow you need to bring in the ln(natural log) that way you can try to solve for e. For example: lne^x+lne^-x=ln3 then the lne cancel out and you come up with x+(-x)=ln3 then you result with 0=ln3 and thats basically how i understand it.
ReplyDelete