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प्रश्न
The domain of \[\cos^{- 1} \left( x^2 - 4 \right)\] is
विकल्प
[3, 5]
[−1, 1]
\[\left[ - \sqrt{5}, - \sqrt{3} \right] \cup \left[ \sqrt{3}, \sqrt{5} \right]\]
\[\left[ - \sqrt{5}, - \sqrt{3} \right] \cap \left[ \sqrt{3}, \sqrt{5} \right]\]
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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