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Find the domain of sin^(-1) (x^2-4)

This question is similar to Question-19 CBSE Class-12 Sample Paper for 2023 Boards

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Transcript

We know that Domain of 〖𝑠𝑖𝑛〗^(βˆ’1) πœƒ 𝑖𝑠 "[–1, 1]" Thus, we can write βˆ’1β‰€πœƒβ‰€1 Putting ΞΈ = π‘₯^2βˆ’4 βˆ’πŸ ≀𝒙^πŸβˆ’πŸ’β‰€πŸ" " Adding 4 on both sides 1+4 ≀π‘₯^2βˆ’4+4≀1" "+ 4 πŸ‘ ≀𝒙^πŸβ‰€"5" Taking square root both sides Β±βˆšπŸ‘ β‰€π’™β‰€Β±βˆšπŸ“ " " So, we can write βˆ’βˆšπŸ“<𝒙 β‰€βˆ’βˆšπŸ‘ and βˆšπŸ‘<𝒙 β‰€βˆšπŸ“ Thus, Domain ofγ€– sinγ€—^(βˆ’1) (π‘₯^2βˆ’4)𝑖𝑠 [βˆ’βˆšπŸ“, βˆ’βˆš(πŸ‘ )]βˆͺ[√(πŸ‘ ), βˆšπŸ“] " "

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.