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Inverse of a function

  1. Jul 27, 2012 #1
    1. The problem statement, all variables and given/known data
    f(x)=3+x2+tan((πx)/2) where -1<x<1....then find f^-1(3)



    2. Relevant equations

    y=3+x2+tan((πx)/2)

    3. The attempt at a solution
    i jave ried to solve first for x and then interchange the x and y,bu i am having problem with the trignometric identity used here.......
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 27, 2012 #2
    Just making sure:

    Is it

    [itex] f(x) = 3 + x^{2} + \tan{\frac{\pi x}{2}} [/itex]

    you mean?
     
  4. Jul 27, 2012 #3
    yea...its tan((pi*x)/2)
     
  5. Jul 27, 2012 #4
    And you're only looking for f^-1(3)? If so, it might be easier to use the definition of an inverse function: What do you know about f(x) if

    [itex] f^{-1}(3) = x[/itex]

    EDIT: Sorry, made a small-ish error there : P
     
    Last edited: Jul 27, 2012
  6. Jul 27, 2012 #5

    Ray Vickson

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    If x2 is supposed to be x2, then you need to write it properly. You can either use the "X2" button on the palette at the top of the input panel, or else write the standard text version x^2. Anyway, if f(x) = 3 you need x^2 + tan(pi*x/2) = 0. Can you see what x must be?

    RGV
     
  7. Jul 27, 2012 #6
    yea but can u show me the whole
    process
     
  8. Jul 27, 2012 #7

    Ray Vickson

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    Who are you responding to? By "u", do you mean "you"? Was your message a question? (It did not end in a question mark!)

    If it was a question, I must say that the answer is NO. Read the Forum rules. We are not permitted to do your work for you; we can just give you hints, which has already been done. Now you need to show some of your own work. If you do that and are still stuck you can come back and ask more questions.

    RGV
     
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