Find the domain of definition of f(x) = cos-1(x2 – 4)

1.	Find the domain of definition of f(x) = cos-1(x2 – 4)
Answer» 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]

Answer»

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]

Discussion