Answer
Domain: $( \frac{1}{2},\ \infty)$
Work Step by Step
We are given:
$f(x)= \frac{(x+1)^{2}}{\sqrt{2x-1}}$
The domain of a function consists of all the values that $x$ is allowed to have. In this case, we can not take the square root of a negative number:
$2x-1\ge 0$
$x\ge \frac{1}{2}$
In addition, we can not have division by $0$:
$2x-1\ne 0$
$x\ne \frac{1}{2}$
Thus the domain is $( \frac{1}{2},\ \infty)$
