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Math Help - Quick question on Inverse Functions

  1. #1
    Junior Member
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    Quick question on Inverse Functions

    Hi,

    I was just wondering if the inverse of f(x)=x^2 would include both positive and negative arms of the square root of x. So would the inverse be plus/minus? or just the positive arm.

    And say I'm working backwards from the function: positive square root of x (just the positive arm). If I were to solve for the inverse of that, would it include both arms of the parabola x^2? Or just the right arm?

    I ask this because I thought the domains and range of the original and inverse function are suppose to switch with one another. And this would only be true if I am with this..

    Just need confirmation. Thanks!!
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  2. #2
    MHF Contributor
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    Talking

    The inverse would include both halves, but would not be a function.

    To get a function as the inverse, you'd need a restriction on x^2 to one half or the other, giving you only one of the halves for the inverse.
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  3. #3
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    Quote Originally Posted by stapel View Post
    The inverse would include both halves, but would not be a function.

    To get a function as the inverse, you'd need a restriction on x^2 to one half or the other, giving you only one of the halves for the inverse.
    So say I'm given the function: y = the (positive) square root of x [so just the positive arm], would the inverse of that function (y=x^2) include just the right (positive) arm as well? Meaning there's a restriction on the domain where x>/=0?

    Thanks!
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