Answer
$D=(-3,\infty)$
The range of $f$ is $\{y| y\geq3\}=[3,+\infty)$
Work Step by Step
We are given: $f(x)=\sqrt x+3$
The domain is: $x+3\geq0 \rightarrow x\geq-3$
$D=(-3,\infty)$
Because $x\geq0$ for all real numbers, we have $x+3\geq3$, so for every output we have $f(x)\geq3$. Thus, the range of f is $\{y| y\geq3\}=[3,+\infty)$
