Question
Download Solution PDFFind the domain of the function y = cos-1 (x2 - 9)
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 - 9) --------(Given)
⇒ x2 - 9 = cos y
As we know that, -1 ≤ cos y ≤ 1, where y ∈ R
⇒ - 1 ≤ x2 - 9 ≤ 1
Adding 9 on all the sides of the inequation we get
⇒ 8 ≤ x2 ≤ 10
We can re-write the above inequation as
⇒ 2√2 ≤ |x| ≤ √10
⇒ x ∈ [-√10, -2√2] ∪ [2√2, √10]
Hence, the domain of the given function is [-√10, -2√2] ∪ [2√2, √10]
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