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Math Help - Having trouble finding domains...

  1. #1
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    Question Having trouble finding domains...

    Find the domain of the following two functions:
    1. f(x) = \sqrt{\log_{0.5}\frac{x+3}{x-1}}

    2.  h(t) = \sqrt{2^{-t} + 1} + \arcsin\frac{2t}{1+t^2}
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  2. #2
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    Quote Originally Posted by xxlvh View Post
    Find the domain of the following two functions:
    1. f(x) = \sqrt{\log_{0.5}\frac{x+3}{x-1}}

    2.  h(t) = \sqrt{2^{-t} + 1} + \arcsin\frac{2t}{1+t^2}
    You should note that the argument inside the square root must be non-negative, that the argument of the logarithm must be non-negative and that the argument of arcsin must be between -1 and 1.

    Can you solve this now?
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  3. #3
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    I have never solved an inequality involving a logarithm
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  4. #4
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    Okay concerning \frac{x+3}{x-1} > 0 I reached a solution of x < -3 or x > 1, hopefully that is correct.

    However, I must be making an error when solving the inequality with the logarithm and I can't quite figure out where...
    \log_{0.5}\frac{x+3}{x-1} > 0

    \log_{0.5}x+3 - \log_{0.5}x-1 > 0

    \log_{0.5}x+3 > \log_{0.5}x-1

    0.5^{\log_{0.5}x+3} > 0.5^{\log_{0.5}x-1}

     x + 3 > x - 1

     x + 2 > x true for all values of x? I'm really lost on this one
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