[tex]\begin{gathered} f(x)=\sqrt[]{2x+7} \\ \text{the root has real values if and only if} \\ 2x+7\ge0 \\ \text{therefore,} \\ 2x\ge0-7 \\ 2x\ge-7 \\ x\ge-\frac{7}{2} \\ x\ge-3.5 \\ \text{Then, the domain is} \\ x\in\lbrack-3.5,\text{ }\infty) \end{gathered}[/tex]
