The domain of the function f x -sin -1log 2 x 2-2 isA- -2-2-B- -2-1-C- -1-2-D- -2-1- -1-2-

The correct option is D [ 2, 1] [1,2] f(x)=sin^ 1 ( log_2 ( x^2/2 ) )ϵ R ⇔ 1 ≤ log_2 ( x^2/2 )≤ 1 ⇔1/2≤x^2/2≤ 2 ⇔ 1 ≤ x^2 ≤ 4 ⇔ x ϵ [ 2, 1] ∪ [1,2] ...

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Byju's Answer

Standard XII

Mathematics

Domain

The domain of...

Question

$T h e d o m a i n o f t h e f u n c t i o n f (x) = s i n^{- 1} (l o g_{2} (\frac{x^{2}}{2})) i s$

[-2,2]

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[-2,-1]

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[1,2]

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[-2,-1] [1,2]

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Solution

The correct option is D
[-2,-1] [1,2]

$f (x) = s i n^{- 1} (l o g_{2} (\frac{x^{2}}{2})) ϵ R \Leftrightarrow - 1 \leq l o g_{2} (\frac{x^{2}}{2}) \leq 1 \Leftrightarrow \frac{1}{2} \leq \frac{x^{2}}{2} \leq 2 \Leftrightarrow 1 \leq x^{2} \leq 4 \Leftrightarrow x ϵ [- 2, - 1] \cup [1, 2]$

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The domain of the function f(x)=sin−1(log2(x22))is

The correct option is D [-2,-1] [1,2] f(x)=sin−1(log2(x22))ϵ R⇔−1≤log2(x22)≤1⇔12≤x22≤2⇔1≤x2≤4⇔xϵ[−2,−1]∪[1,2]

$T h e d o m a i n o f t h e f u n c t i o n f (x) = s i n^{- 1} (l o g_{2} (\frac{x^{2}}{2})) i s$

The correct option is D
[-2,-1] [1,2]

$f (x) = s i n^{- 1} (l o g_{2} (\frac{x^{2}}{2})) ϵ R \Leftrightarrow - 1 \leq l o g_{2} (\frac{x^{2}}{2}) \leq 1 \Leftrightarrow \frac{1}{2} \leq \frac{x^{2}}{2} \leq 2 \Leftrightarrow 1 \leq x^{2} \leq 4 \Leftrightarrow x ϵ [- 2, - 1] \cup [1, 2]$