Question 21 (Choice 2) - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 13, 2024 by Teachoo

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〗^(−1) 𝜃 𝑖𝑠 "[–1, 1]" Thus, we can write −1≤𝜃≤1 Putting θ = 𝑥^2−4 −𝟏 ≤𝒙^𝟐−𝟒≤𝟏" " Adding 4 on both sides 1+4 ≤𝑥^2−4+4≤1" "+ 4 𝟑 ≤𝒙^𝟐≤"5" Taking square root both sides ±√𝟑 ≤𝒙≤±√𝟓 " " So, we can write −√𝟓<𝒙 ≤−√𝟑 and √𝟑<𝒙 ≤√𝟓 Thus, Domain of〖 sin〗^(−1) (𝑥^2−4)𝑖𝑠 [−√𝟓, −√(𝟑 )]∪[√(𝟑 ), √𝟓] " "

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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