Answer
$-2\leq t\leq 3$
Work Step by Step
$g(t)$ is defined for all real $t$ where $3-t\geq0$ and $t+2\geq0$, since only the square roots of positive numbers are real
When $3-t\geq0, t\leq3$
When $t+2\geq0, t\geq-2$
Both conditions can only be fulfilled in the domain $-2\leq t\leq 3$
