#### Answer

Domain: $(-\infty, +\infty)$
Range: $(-\infty, -2] \cup [2, +\infty)$

#### Work Step by Step

RECALL:
The cosecant function $y=\csc{x}$ has:
(1) $(-\infty, +\infty)$ (the set of real numbers) as its domain; and
(2) $(-\infty, -1] \cup [1, +\infty)$ as its range. The value of the function is never in the interval $(-1, 1)$.
Thus, the domain of the given function is also the set of real numbers.
The given function has $2$ as a multiplier outside the cosecant function.
The value of the given function is will never be between $-2$ and $2$ so its range is $(-\infty, -2] \cup [2, +\infty)$.