#### Answer

the domain is: $(-1,\ \infty)$

#### Work Step by Step

We are given:
$f(x)=3x- \frac{2}{\sqrt{x+1}}$
We can not take the square root of a negative number, so:
$x+1\geq 0$
$ x\geq -1$
We also can't have a zero denominator:
$x+1\ne 0$
$ x\ne -1$
Thus overall: $ x\gt -1$.
Therefore, the domain is: $(-1,\ \infty)$.