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Math Help - Inverse problem

  1. #1
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    Joined
    Oct 2011
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    153

    Inverse problem

    Find the inverse of f(x) = x/(sqrt(x^2+7)

    This is what I did so far:
    I switched the variables.
    y = x/(sqrt(x^2+7))
    Switch x and y,
    x = y/(sqrt(y^2+7))
    Square both sides,
    x^2 = y^2/(y^2+7)
    x^2y^2+7x^2 = y^2
    Then I got the wrong answer, so I stopped here.

    I was told to go on like this, which is the answer.
    Though somehow it just went to 7x^2 and a 1-x^2 came along.
    Like how did they do that?

    y^2 = 7x^2/(1-x^2)
    y = [7x^2/(1-x^2)]^(1/2)

    Can someone explain or show in another way?
    Thanks!
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  2. #2
    Member
    Joined
    Mar 2013
    From
    BC, Canada
    Posts
    95
    Thanks
    15

    Re: Inverse problem

    Quote Originally Posted by Chaim View Post
    Find the inverse of f(x) = x/(sqrt(x^2+7)

    This is what I did so far:
    I switched the variables.
    y = x/(sqrt(x^2+7))
    Switch x and y,
    x = y/(sqrt(y^2+7))
    Square both sides,
    x^2 = y^2/(y^2+7)
    x^2y^2+7x^2 = y^2
    You are correct up to this point. You said that "then I got the wrong answer", so, did you attempt to solve for y? What did your attempt look like? Perhaps if you show some of your work, we can help you and explain where the 1-x^2 expression came from.
    Thanks from HallsofIvy
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