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Math Help - Find the range

  1. #1
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    Find the range

    Find the range of the following function.

    f(x) = (4+x)/(3-2x)

    Looking for something like this

    y= x^2
    x = +/- sqrt(y)

    y>0
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  2. #2
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    Quote Originally Posted by glover_m View Post
    Find the range of the following function.

    f(x) = (4+x)/(3-2x)

    Looking for something like this

    y= x^2
    x = +/- sqrt(y)

    y>0
    range of f(x) will be the domain of f^{-1}(x)

    y = \frac{4+x}{3-2x}

    swap variables ...

    x = \frac{4+y}{3-2y}

    solve for y ...

    3x - 2xy = 4+y

    3x - 4 = y + 2xy

    3x-4 = y(1 + 2x)

    \frac{3x-4}{1+2x} = y = f^{-1}(x)

    domain of the inverse function is all reals except x = -\frac{1}{2}

    so ... range of f(x) is all reals except y = -\frac{1}{2}
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  3. #3
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    thanks so much
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