Answer
$(-1, +\infty)$
Work Step by Step
The given function is undefined when:
(i) the denominator of $\dfrac{2}{\sqrt{x+1}}$ is equal to 0; and
(ii) the radicand $x+1$ is negative.
Note that:
(1) The denominator $\sqrt{x+1}$ is equal to 0 when $x=-1$.
(2) The radicand $x+1$ is negative when $x \lt -1$.
Thus, the given function is defined when $x$ is greater than $-1$.
Since $x$ cannot be less than or equal to $-1$, then the domain of the given function is the set of real numbers greater than $-1$.
In interval notation, the domain is $(-1, +\infty)$.