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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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