#### Answer

$\left[ -\dfrac{7}{2},\infty \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
The domain of the given function, $
f(x)=\sqrt{2x+7}
,$ is all values of $x$ for which the radicand is non-negative. Express the answer in interval notation.
$\bf{\text{Solution Details:}}$
Since the radicand of a radical with an even index has to be non-negative, then
\begin{array}{l}\require{cancel}
2x+7\ge0
\\\\
2x\ge-7
\\\\
x\ge-\dfrac{7}{2}
.\end{array}
Hence the domain is $
\left[ -\dfrac{7}{2},\infty \right)
.$