Given function f(x) = cos-1(x2 – 4)
As, we know domain of cos-1(x2 – 4) lies in the interval [-1, 1]
So, we can write
-1 ≤ x2 – 4 ≤ 1
4 – 1 ≤ x2 ≤ 1 + 4
3 ≤ x2 ≤ 5
± √3 ≤ x ≤ ± √5
– √5 ≤ x ≤ – √3 and √3 ≤ x ≤ √5
So, domain of cos-1(x2 – 4) is [-√5, – √3] ∪ [√3, √5]