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Math Help - what's inverse of this function?

  1. #1
    Like a stone-audioslave ADARSH's Avatar
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    what's inverse of this function?

    CAN U TELL THE INVERSE OF
    X-SIN(X)?
    THANK U
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  2. #2
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    Hello, ADARSH!

    First of all, release your CAPS LOCK . . .
    All upper-case is very annoying ... and juvenile.


    Can you tell the inverse of: . f(x) \:=\:x-\sin(x) ? . . . . no

    We are required to solve for y\!:\;\;y - \sin y \:=\:x

    This is a transcendental equaton . . . there is no elementary solution.

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  3. #3
    Like a stone-audioslave ADARSH's Avatar
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    Wink

    I have recieved the answer as
     <br />
X+sin(X)<br />
    Its mirror image
    of X-sin(X)about  x=y
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  4. #4
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    Quote Originally Posted by ADARSH View Post
    I have recieved the answer as
     <br />
X+sin(X)<br />
    Its mirror image
    of X-sin(X)about  x=y
    is that so?

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  5. #5
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    Before I continue, let me say how dumb I think this question/answer is.
    However, the posted answer is in fact correct.
    If you graph the inverse correctly it is easy to see.
    The reflection in the line y=x is (x,y) \to (y,x).
    Attached Thumbnails Attached Thumbnails what's inverse of this function?-inverse.gif  
    Last edited by Plato; September 6th 2008 at 03:49 PM.
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  6. #6
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    are you saying that y = x+\sin{x} is the inverse of y = x-\sin{x} ?

    here is a correct graph of y = x-\sin{x} and its inverse x = y-\sin{y} ...

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  7. #7
    Like a stone-audioslave ADARSH's Avatar
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    I also got the same graph as Skeeter fr  x+sinx
    and that's why I posted this quest.
    if reflection abt
     x=y always the inverse
    than wat abt
    sinx-x
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  8. #8
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    Quote Originally Posted by skeeter View Post
    are you saying that y = x+\sin{x} is the inverse of y = x-\sin{x} ?
    Absolutely not! Soroban has is correct. There is no elementary inverse possible.
    However, in parametric form \left( {t,t + \sin (t)} \right)\,\& \,\left( {t + \sin (t),t} \right) are reflections of each other in the line y=x and as such act as an inverse.
    In this new graphic, that point is illustrated using t=2.
    Attached Thumbnails Attached Thumbnails what's inverse of this function?-grid2.gif  
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  9. #9
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    my mistake ...

    when you said

    However, the posted answer is in fact correct.
    I thought you were talking about the OP's response to Soroban's response.
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