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Math Help - Finding the domain

  1. #1
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    Finding the domain

    The question:
    Determine f/g, and give the domain.

    f(x) = \sqrt{x -1}
    g(x) = x - \sqrt{x + 1}

    I did:

    \frac{\sqrt{x-1}}{x - \sqrt{x + 1}}

    And I found that x had to be >= 1 (since you can't square root a negative value). I wrote [1, inf) as my answer. However, the answer is [1, \frac{1 + \sqrt{5}}{2}) U (\frac{1 + \sqrt{5}}{2}, \inf)

    I'm not sure how this answer was calculated. Any assistance would be awesome. Thanks.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    x-sqrt(x+1)!=0
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  3. #3
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    Aha! That was a massive oversight.

    For other people looking at this thread:

    x - \sqrt{x + 1} = 0
    x + 1 = x^2
    x^2 -x - 1 = 0

    Find roots/zeros using quadratic formula:

    \frac{1 +- \sqrt{1 - 4(1)(-1)}}{2}
    \frac{1 +- \sqrt{5}}{2}

    Erm, how do I do "+ or -" in Latex so this quadratic eqn makes more sense?
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  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
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    but solution with minus is not induced(why?)
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  5. #5
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    Because we already know that x must be larger than or equal to 1 to satisfy the numerator.
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  6. #6
    MHF Contributor Also sprach Zarathustra's Avatar
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    Job well done!


    "Erm, how do I do "+ or -" in Latex so this quadratic eqn makes more sense?"

    \pm

    \pm
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