Question

What is the domain of the function

Answer 1

$\sqrt{5+x}$ is defined as long as $5+x\ge0$, or $x\ge-5$. However, $\dfrac1x$ is undefined when $x=0$. This point is contained in the set $\{x|x\ge-5\}$, so we need to exclude it. We can write the domain in several ways.

$\{x|x\ge-5~\land~x\neq0\}$
$-5\le x$
$[-5,0)\cup(0,\infty)$