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Homework Help: Derivative of inverse function (HELP PLEASE)

  1. Dec 16, 2007 #1
    Ok,

    We are asked to find

    (f-1(3))' for f(x) = 3 + x^2 + tan(x*pi/2)

    I think we are supposed to use the formula (f-1(x))' = 1/f'(f-1(x))

    But I am not sure how to get f-1(3).
    If someone can show me how to get that, it would be extremely helpful for me to understand how this works.

    Thank you.
     
  2. jcsd
  3. Dec 16, 2007 #2
    What book are you using? You ask a lot of questions ... either your book really sucks, your teacher sucks, or you're not studying enough.
     
  4. Dec 16, 2007 #3
    I think what rocophysics is saying, is that if you showed a little more work, we'd be more apt to help.

    I would certainly think that he was not discouraging you from asking a lot of questions. God knows I do.

    Casey
     
  5. Dec 16, 2007 #4
    My book doesn't go over this for some reason, it goes straight into inverse trig functions. I cannot get any firther without getting throught that first step:

    SO, 3 + x^2 + tan(x*pi/2) = 3

    x^2 + tan(x*pi/2) = 0

    I don't know how to find out when this happens...
    If anyone can show me how, i would be able to gain some insight into this. If I had money I would pay someone to show me, but I am broke ok?
     
  6. Dec 16, 2007 #5
    What happens when x=0?

    Casey
     
  7. Dec 16, 2007 #6
    f(x) = 3 + x^2 + tan(x*pi/2)

    can you find f-1(x)? That would be a start
     
  8. Dec 16, 2007 #7
    No, I can't. Can you please show me how, that would be a tremendous help.

    Also, what is the curve of r = sqrt(sin(X)) ?

    I could not find it on my textbook.
     
  9. Dec 16, 2007 #8

    HallsofIvy

    User Avatar
    Science Advisor

    If you are not going to pay any attention to the responses to your questions why ask?

    As Casey said, what bloody happens when x= 0???

    What do you mean by "what is the curve of r= sqrt(sin(X))? I know how to find the curve of a function in Cartesian coordinates and even in polar coordinates- but that is neither. You have to have some kind of coordinate system before you can talk about the "curve" corresponding to a function or equation!
     
  10. Dec 16, 2007 #9
    hint: to find f-1(x), switch x and y everywhere in the equation and solve for y
     
    Last edited: Dec 16, 2007
  11. Dec 16, 2007 #10
    Last edited: Dec 16, 2007
  12. Dec 16, 2007 #11
    it is just it man ==> r^2 = sqrt(sin(X))
    And what happens when x= 0????

    <edit: MIH>
     
    Last edited by a moderator: Dec 16, 2007
  13. Dec 16, 2007 #12
    <edit:MIH>

    What exactly does it mean to say that x=0? How would you perform that operation mathematically?
     
    Last edited by a moderator: Dec 16, 2007
  14. Dec 16, 2007 #13
    As I speak, tears are rolling down my cheeks. I have used x = 0 and arrived at the answer!


    EDIT:

    for the graph = x^2 + y^2 = sin x???
    I don't really know what to do. We are just asked to find the curve bounded by r = (sin(x)^1/2 for 0 <= x <= pi/3

    any hints????
     
    Last edited: Dec 16, 2007
  15. Dec 16, 2007 #14
    f-1(x) of a function is usually done like this:

    f(x) = y = x+1 for example

    1.) Switch x's and y's, so we now have x = y+1
    2.) Solve for y, so y = x-1 = f-1(x)
     
  16. Dec 16, 2007 #15
    You should check out some Precalculus books from the library.

    It's always handy to have around.
     
  17. Dec 16, 2007 #16
    for the graph = x^2 + y^2 = sin x???
    I don't really know what to do. We are just asked to find the curve bounded by r = (sin(x)^1/2 for 0 <= x <= pi/3

    any hints????
     
  18. Dec 16, 2007 #17
    Does it say find the curve bounded by....? Or the area?

    Casey
     
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