Answer
domain: $[4,7) \cup (7, +\infty)$
Work Step by Step
$P(t)=\frac{\sqrt {t-4}}{3t-21}$
$t-4\geq0$
$t\geq4$
$3t-21=0$
$3t=21$
$t=7$
$t\ne7$
Therefore, the domain of a function is set s of interval notation $4\leq x \lt 7$ and $x\gt7$ or $[4,7) \cup (7, +\infty)$
