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    I am required to find the Domain of \frac{f}{g}

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

    I have found the following Domains;

    D(f) = [0,+∞]
    D(g) = [-∞,1]

    to find Domain of \frac{f}{g}

    D(\frac{f}{g} ) = D(f) n D(g) - g(x) = 0 Is this correct?

    If this is correct then

    D(f) n D(g) = [0,1]

    Where g(x) = 0 x must = 1

    hence D(\frac{f}{g}) = [0,1] - 1 ??

    crashMATHS

    Any help is welcome. Thank you in advance.
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    (Original post by NoahMal)
    ...
    That right, though your notation can be much better.

    \displaystyle \mathrm{Dom} \left( \frac{f}{g} \right) = \mathrm{Dom}(f) \cap \mathrm{Dom}(g) \setminus \{ x \in \mathrm{Dom}(g) : g(x) =0 \}

    So your answer can just be rewritten as \displaystyle \mathrm{Dom} \left( \frac{f}{g} \right) = [0,1)
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    (Original post by RDKGames)
    That right, though your notation can be much better.

    \displaystyle \mathrm{Dom} \left( \frac{f}{g} \right) = \mathrm{Dom}(f) \cap \mathrm{Dom}(g) \setminus \{ x : g(x) =0 \}

    So your answer can just be rewritten as \displaystyle \mathrm{Dom} \left( \frac{f}{g} \right) = [0,1)
    Thank you for this, but I'm still confused with what I do with x : g(x) = 0 with the final notation?
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    (Original post by NoahMal)
    Thank you for this, but I'm still confused with what I do with x : g(x) = 0 with the final notation?
    The backlash means 'except from the set...' and then I proceed to define a set with elements x in the domain of g, such that (which is what the colon means) we have g(x)=0. So overall it just means "Intersection of the two domains except the set of values for which the denominator is 0"

    The set \{ x \in \mathrm{Dom}(g) : g(x)=0 \} can also be just simplified to, and replace by, \{ 1 \}
 
 
 
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