IMathAS-libretexts

Given $\displaystyle {f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}-{4}}}}$ and $\displaystyle {g{{\left({x}\right)}}}={\frac{{{1}}}{{{x}-{6}}}}$ , determine the Domain of $\displaystyle {f{{\left({g{{\left({x}\right)}}}\right)}}}$ . Write your answer in Interval Notation. Round your answers to two decimal places as needed.

$\displaystyle {\left(-\infty,{6}\right)}{U}{\left({6},{6.25}\right)}{U}{\left({6.25},\infty\right)}$
$\displaystyle {\left(-\infty,{4}\right)}{U}{\left({4},{6}\right)}{U}{\left({6},\infty\right)}$
$\displaystyle {\left[{6},{6.25}\right]}$

$\displaystyle {\left({4},{6}\right)}{U}{\left({6},{6.25}\right)}$
$\displaystyle {\left(-\infty,{0}\right)}{U}{\left({0},\infty\right)}$
$\displaystyle {\left(-\infty,{4}\right)}{U}{\left({6},\infty\right)}$

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