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Math Help - Find the Domain

  1. #1
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    Find the Domain

    If f(x)=\sqrt{x+4} and g(x)=\sqrt{x-1}, find the domain of \,\frac{f}{g}
     \left(\frac{f}{g}\right)(x)=\frac{\sqrt{x+4}}{\sqr  t{x-1}}=\sqrt{\frac{x+4}{x-1}}

    So a radical is only when the value of the expression is greater than  0, I would have thought that to find the domain, all I need to do is solve this rational inequality \frac{x+4}{x-1}\geq 0, whose solution is (-\infty, -4]\cup (1, \infty), but, my solution manual says that the domain is actually (1, \infty). Why is this so?

    Thanks ,

    James
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  2. #2
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    Quote Originally Posted by james121515 View Post
    If f(x)=\sqrt{x+4} and g(x)=\sqrt{x-1}, find the domain of \,\frac{f}{g}
     \left(\frac{f}{g}\right)(x)=\frac{\sqrt{x+4}}{\sqr  t{x-1}}=\sqrt{\frac{x+4}{x-1}}

    my solution manual says that the domain is actually (1, \infty). Why is this so?
    The manual is correct.
    (-\infty,-4) is not a subset of the domain of either f\text{ or }g.
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