TS EAMCET · Maths · Functions
The domain of the real valued function \(f(x)=\sin ^{-1}\left(\log _2\left(\frac{x^2}{2}\right)\right)\) is
- A \([-2,0) \cup(1,2]\)
- B \([-2,-1] \cup[1,2]\)
- C \([-1,0] \cup[1,2]\)
- D \([1, \infty) \cup(-2,0)\)
Answer & Solution
Correct Answer
(B) \([-2,-1] \cup[1,2]\)
Step-by-step Solution
Detailed explanation
\(f(x)=\sin ^{-1}\left(\log _2\left(\frac{x^2}{2}\right)\right)\) We know domain of \(\sin ^{-1} x\) is \([-1,1]\) \(\therefore-1 \leq \log _2\left(\frac{x^2}{2}\right) \leq 1\)…
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