Question

Determine the domain of f(x)=√2x+7 in set builder notation

Answer 1

`\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-(7)/(2) \\ x\ge-3.5 \\ \text{Then, the domain is} \\ x\in\lbrack-3.5,\text{ }\infty) \end{gathered}`