Your function is √(x² - 4).
The part inside the sqrt must be non-negative, thus, solve: x² - 4 ≥ 0.
Then, algebraically, you get: x² ≥ 4 ---> |x| ≥ 2 ---> -2>x or 2<x.
Hence, the domain of your function is (-∞,-2) U (2,∞).
((( i.e. from negative infinity to -2, and then from 2 to infinity )))
