Darian Hubbard

2022-07-22

Find the following

$a\right)\left(f+g\right)\left(x\right)=\phantom{\rule{0ex}{0ex}}b\right)\left(f-g\right)\left(x\right)=\phantom{\rule{0ex}{0ex}}c\right)\left(fg\right)\left(x\right)=\phantom{\rule{0ex}{0ex}}d\right)\left(f/g\right)\left(x\right)=$
What is the domain of f/g?

neobuzdanio

Expert

For domain of (f/g)(x)
${x}^{2}\ne 0$
$⇒x\ne 0$ (i)
and
${x}^{2}-16\ge 0\phantom{\rule{0ex}{0ex}}⇒\left(x+4\right)\left(x-4\right)\ge 0\phantom{\rule{0ex}{0ex}}⇒x\in \left(-\mathrm{\infty },-4\right],\left[4,\mathrm{\infty }\right)$ (ii)
From (i) and (ii)
Domain of $f/g⇒\left(-\mathrm{\infty },-4\right],\left[4,\mathrm{\infty }\right)$

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