Question
Download Solution PDFFind the domain of the function y = cos-1 (x2 - 4)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If cos-1 x = y then x = cos y
Calculation:
As we know that, if cos-1 x = y then x = cos y
So,y = cos-1 (x2 - 4) --------(Given)
⇒ x2 - 4 = cos y
As we know that, -1 ≤ cos y ≤ 1, where y ∈ R
⇒ - 1 ≤ x2 - 4 ≤ 1
Adding 4 on all the sides of the inequation we get
⇒ 3 ≤ x2 ≤ 5
We can re-write the above inequation as
⇒ √3 ≤ |x| ≤ √5
⇒ x ∈ [-√5, -√3] ∪ [√3, √5]
Hence, the domain of the given function is [-√5, -√3] ∪ [√3, √5]
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