The domain of the function f ( x ) = sin − 1 ( lo g 2 ( 2 x 2 ) ) is

f ( x ) = sin − 1 ( lo g 2 ( 2 x 2 ) ) ∈ R ⇔ − 1 ≤ lo g 2 ( 2 x 2 ) ≤ 1 ⇔ 2 1 ≤ 2 x 2 ≤ 2 ⇔ 1 ≤ x 2 ≤ 4 ⇔ x ∈ [ − 2 , − 1 ] ∪ [ 1 , 2 ]

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MathematicsFunctionsDomain-RangeMedium2 minQB

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The domain of the function $f (x) = sin^{- 1} (lo g_{2} (\frac{x ^{2}}{2}))$ is

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$f (x) = sin^{- 1} (lo g_{2} (\frac{x ^{2}}{2})) \in R \Leftrightarrow - 1 \leq lo g_{2} (\frac{x ^{2}}{2}) \leq 1 \Leftrightarrow \frac{1}{2} \leq \frac{x ^{2}}{2} \leq 2$

$\Leftrightarrow 1 \leq x^{2} \leq 4 \Leftrightarrow x \in [- 2, - 1] \cup [1, 2]$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Domain-Range

⏱ 2mℹ️ Source: QB

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