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Inverse function

  1. Apr 24, 2010 #1
    The condition for the inverse function, f^(-1) to happen is function , f is one-one .

    S0 consider this function , f(x)=x^2-5 , which is NOT a one-one function , and

    f^(-1)=y

    x=f(y)

    x=y^2-5

    y^2=x+5

    [tex]f^{-1}(x)=\pm\sqrt{x+5}[/tex]

    Seems that the inverse function of f exists without satisfying that condition .
     
  2. jcsd
  3. Apr 24, 2010 #2

    Cyosis

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    That inverse function you found is not even a function. For every x there are two values of y. For it to be a function there can only be one value of y for every x.

    Secondly f(x) in general is not a function, but just a number in its codomain. Your function f is given by [itex]f:A\rightarrow B, f(x)=x^2-5[/itex]. With A its domain and B its codomain. Depending on A and B f can have an inverse.

    example:

    [tex]
    f:[0,1] \rightarrow [-5,-4]; f(x)=x^2-5
    [/tex]

    this function has an inverse.

    [tex]
    f:[-1,1] \rightarrow [-5,-4]; f(x)=x^2-5
    [/tex]

    this one does not.
     
  4. Apr 24, 2010 #3

    thanks ! I just realised it can have inverse when its broken into half .
     
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