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Math Help - Domain of function?

  1. #1
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    Domain of function?

    Is the domain of

    f(x)= 1/sqrt(6-x)(5+x)

    (-5,6) or (5,6) ?
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  2. #2
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    Quote Originally Posted by offahengaway and chips View Post
    Is the domain of

    f(x)= 1/sqrt(6-x)(5+x)

    (-5,6) or (5,6) ?
    f\left( x \right) = \frac{1}<br />
{{\sqrt {\left( {6 - x} \right)\left( {5 + x} \right)} }}

    For domain, the term inside the square-root should be non-negative.

    so, (6-x)(5+x)\ge 0

    therefore,  6-x \ge 0 \;\;and \;\; 5+x \ge 0

    \Rightarrow 6 \ge x \;\; and \;\; x \ge -5

    \Rightarrow -5 \le x \le 6

    \Rightarrow x \in (-5, 6)

    Also,  6-x \le 0 \;\;and \;\; 5+x \le 0

    \Rightarrow x \le -5 \;\; and \;\; x \ge 6

    \Rightarrow No \;\;Solution
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  3. #3
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    That has to be wrong, 'cause we require that (6-x)(5+x)>0. After some simple calculations we have,

    \begin{aligned}<br />
   30+x-x^{2}&>0 \\ <br />
  x^{2}-x-30&<0 \\ <br />
  (2x-1)^{2}-121&<0 \\ <br />
  -11<2x-1&<11,<br />
\end{aligned}

    and we happily get -10<2x<12\implies -5<x<6, which is the required domain.
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