Class 12 Inverse Trigonometric Functions · Short Answer2 Marksdomains_and_ranges
Class 12 Maths · Inverse Trigonometric Functions · Short Answer #53
Find the real domain of \(y=\sin^{-1}(x^2-4)\).
![Closed intervals [−√5,−√3] and [√3,√5].](/data/assets/inverse-trigonometric-functions-1/arcsin-domain-number-line.svg)
✅ Step-by-Step Solution
Final Answer: [−√5,−√3]∪[√3,√5]
- The arcsine argument must satisfy −1≤x²−4≤1.
- Adding 4 gives 3≤x²≤5, equivalently √3≤|x|≤√5.
- Thus the domain is [−√5,−√3]∪[√3,√5], including all four endpoints.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The arcsine argument must satisfy −1≤x²−4≤1.
- [1 mark] Adding 4 gives 3≤x²≤5, equivalently √3≤|x|≤√5.
- [0.5 marks] Thus the domain is [−√5,−√3]∪[√3,√5], including all four endpoints.
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