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The Domain of Cos − 1 ( X 2 − 4 ) is (A) [3, 5] (B) [−1, 1] (C) [ − √ 5 , − √ 3 ] ∪ [ √ 3 , √ 5 ] (D) [ − √ 5 , − √ 3 ] ∩ [ √ 3 , √ 5 ] - Mathematics

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प्रश्न

The domain of  \[\cos^{- 1} \left( x^2 - 4 \right)\] is

 

विकल्प

  • [3, 5]

  • [−1, 1]

  •  \[\left[ - \sqrt{5}, - \sqrt{3} \right] \cup \left[ \sqrt{3}, \sqrt{5} \right]\]

  •  \[\left[ - \sqrt{5}, - \sqrt{3} \right] \cap \left[ \sqrt{3}, \sqrt{5} \right]\]

MCQ
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उत्तर

The domain of \[\cos^{- 1} \left( x \right)\] is [-1, 1]

\[\therefore - 1 \leq x^2 - 4 \leq 1\]
\[ \Rightarrow - 1 + 4 \leq x^2 - 4 + 4 \leq 1 + 4\]
\[ \Rightarrow 3 \leq x^2 \leq 5\]
\[ \Rightarrow \pm \sqrt{3} \leq x \leq \pm \sqrt{5}\]
\[ \Rightarrow x \in \left[ - \sqrt{5}, - \sqrt{3} \right] \cup \left[ \sqrt{3}, \sqrt{5} \right]\]

Hence, the correct answer is option (c).

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अध्याय 4: Inverse Trigonometric Functions - Exercise 4.16 [पृष्ठ १२२]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 4 Inverse Trigonometric Functions
Exercise 4.16 | Q 34 | पृष्ठ १२२

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