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Thread: inverse of a piecewise function

  1. #1
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    inverse of a piecewise function

    Hi, if I have a piecewise function such as:

    f(x) = (x-1)^2 if x>1
    or tan(x) if -π/2 < x < 0

    If I want want to find the inverse, do I simply calculate the inverse for each of piecewise operations ?
    eg. (x-1)^2 has the inverse y = 1 +- sqrt(x)
    and tan(x) has the inverse tan^-1(x)

    is it is straightforward as that or I am missing something ?
    thanks for any help.
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    Re: inverse of a piecewise function

    Quote Originally Posted by fran1942 View Post
    Hi, if I have a piecewise function such as:

    f(x) = (x-1)^2 if x>1
    or tan(x) if -π/2 < x < 0

    If I want want to find the inverse, do I simply calculate the inverse for each of piecewise operations ?
    eg. (x-1)^2 has the inverse y = 1 +- sqrt(x)
    and tan(x) has the inverse tan^-1(x)

    is it is straightforward as that or I am missing something ?
    the restriction placed on the domain of the original function will be the range of the inverse function ...

    for f(x) = (x-1)^2 , x > 1 ; f^{-1}(x) = 1 + \sqrt{x} , x > 0

    (note: why is 1 - \sqrt{x} not used?)

    for f(x) = \tan{x} , -\frac{\pi}{2} < x < 0 ; f^{-1}(x) = \tan^{-1}{x} , x < 0
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