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Math Help - Largest possible domain

  1. #1
    Senior Member Stroodle's Avatar
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    Largest possible domain

    Hey there, I'm just trying to work out how to find the largest possible domain to the following function algebraically.

    f(x)=\sqrt{\frac{x-1}{x+2}}

    The way I've been going about it is:

    x-1 must be greater than zero, so x\geq1

    x+2 must be greater than zero, so x\geq-2

    and \sqrt{x+2} can't equal zero, meaning, for this part, x can be any real number besides -2

    From this I get the domain of \left [1,\infty\right )

    Which is not the complete domain stated in the answer. I must be missing something...

    Thanks for your help
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  2. #2
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    Hi Stroodle
    Quote Originally Posted by Stroodle View Post
    The way I've been going about it is:

    x-1 must be greater than zero, so x\geq1

    x+2 must be greater than zero, so x\geq-2
    Your mistake is here because (x-1) and (x+2) can be less than zero at the same time. What you should do is :

    \frac{x-1}{x+2}\geq 0
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  3. #3
    Senior Member Stroodle's Avatar
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    Ahh, of course

    Thanks heaps for that!
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  4. #4
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    To solve \frac{x-1}{x+2}\geq 0,

    you need to consider three ranges, x<-2, -2<x<1 and x>1.

    Choose the range of x s.t. both (x-1) and (x+2) are positive, and that will be x<-2 and x>1. Also, the fraction is equal to zero when x=1.

    Hence, the largest possible domain is (-\infty,-2)\cup[1,\infty)
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  5. #5
    Senior Member Stroodle's Avatar
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    I'm fine with that part, just stupidly overlooked that both the numerator and denominator could be negative
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