Answer
The domain is {$t|t\geq4, t\ne7$}.
Work Step by Step
Requirement (1)
For a fraction to be defined, the denominator cannot be equal to $0$.
Thus,
$3t-21\ne0$
$3t-21+21\ne0+21$
$3t\ne21$
$t\ne7$
Requirement (2)
For a square root to be defined, the function inside the root must be greater than or equal to $0$.
Thus,
$t-4\geq0$
$t-4+4\ge0+4$
$t\geq4$
The two requirements can be applied together, to define the domain:
$$t\ne7 \text{ and } t\geq4$$
Therefore, the domain of the given function is {$t|t\geq4, t\ne7$}.
