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Math Help - Help with an Inverse Equation

  1. #1
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    Help with an Inverse Equation

    I am really stumped on this homework question and I am trying to better understand how to find the inverse, domain, and range.

    The equation g(x) = -2x/(-7x-3). I feel like I am not going about getting the inverse the right way to begin with.

    Thank you

    -Rick
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  2. #2
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    Re: Help with an Inverse Equation

    g(x) = y = \frac{2x}{7x+3}

    x = \frac{2y}{7y+3}

    x(7y+3) = 2y

    7xy+3x = 2y

    3x = 2y - 7xy

    3x = y(2 - 7x)

    y = g^{-1}(x) = \frac{3x}{2-7x}
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  3. #3
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    Re: Help with an Inverse Equation

    Thank you very much for the help - I was multiplying wrong on one side. As far as interval notation for the domain and range goes how would I indicate both with the parenthesis, brackets and U? I believe the domain to not include 2/7 but I am unsure how to find the range once I graph it and to correctly notate both.

    Thanks again!
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  4. #4
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    Re: Help with an Inverse Equation

    for g(x) , 7x+3 \ne 0 ...

    domain: \left(-\infty, -\frac{3}{7} \right) \cup \left(-\frac{3}{7} , \infty \right)

    the range of g(x) is the domain of g^{-1}(x)
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