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Find the domain of the function $f(x)=\\sqrt{\\frac{\\var{a}-x}{x+\\var{b}}}$.
", "advice": "A square root is only defined for positive values, so we need to solve the inequality $g(x)=\\frac{\\var{a}-x}{x+\\var{b}}\\geq 0$. We make a sign chart for the rational function $g$
\nThis results in the following sign chart:
\n$x$ | \n\n | $\\var{-b}$ | \n\n | $\\var{a}$ | \n\n |
$g(x)$ | \n$-$ | \n\\ | \n$+$ | \n0 | \n$-$ | \n
So, the domain is given by $]\\var{-b},\\var{a}]$.
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\nInstructions on entering your answer:
\nYou will need to fill out 4 parts of an interval:
\nDo not round values, enter a fraction if necessary.
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