College Algebra 7th Edition

Domain: $( \frac{1}{2},\ \infty)$
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 $( \frac{1}{2},\ \infty)$