Question -
Answer -
Given f(x) = cos -1 (x2 –4)
We know that domain ofcos-1 (x2 – 4) lies in the interval [-1, 1]
Therefore, we canwrite as
-1 ≤ x2 –4 ≤ 1
4 – 1 ≤ x2 ≤1 + 4
3 ≤ x2 ≤5
±√ 3 ≤ x ≤ ±√5
– √5 ≤ x ≤ – √3 and √3≤ x ≤ √5
Therefore domain ofcos-1 (x2 – 4) is [- √5, – √3] ∪ [√3, √5]