Find the domain of the function f(x) = sqrt(sqrt(x^2 - 16) + 3).
We must have that
sqrt (x^2 - 16) + 3 ≥ 0
All we really need to worry about is that x^2 - 16 ≥ 0
This will be true on two intervals
(-inf , -4 ] U [ 4 , inf) = the domain
See the graph here ; https://www.desmos.com/calculator/htuz2jh2j9