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Thread: Inverse function Q

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    Inverse function Q

    How to find inverse of function with restricted domain?

    g(x)= x^2 - 4x ; x >= 2
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    Quote Originally Posted by NeedHelp18 View Post
    How to find inverse of function with restricted domain?

    g(x)= x^2 - 4x ; x >= 2
    y = x^2 - 4x

    swap variables ...

    x = y^2 - 4y

    complete the square and solve for y ...

    x + 4 = y^2 - 4y + 4

    x + 4 = (y - 2)^2

    \pm \sqrt{x + 4} = y - 2

    y = \pm \sqrt{x + 4} + 2

    since x \geq 2 in the original function, y \geq 2 for the inverse

    g^{-1}(x) = \sqrt{x + 4} + 2
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