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TS EAMCET · Maths · Functions

The domain of the function \(f(x)=\sin ^{-1}\left(\log _2\left(\frac{x^2}{2}\right)\right)\) is

  1. A \([-2,0) \cup(0,1)\)
  2. B \([1, \infty) \cap[-2,2]\)
  3. C \([-2,-1] \cup[1,2]\)
  4. D \((-\infty, 1] \cap[-2,2]\)
Verified Solution

Answer & Solution

Correct Answer

(C) \([-2,-1] \cup[1,2]\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & f(x)=\sin ^{-1}\left(\log _2\left(\frac{x^2}{2}\right)\right) \\ \Rightarrow & -1 \leq \log _2\left(\frac{x^2}{2}\right) \leq 1 \\ \Rightarrow & \frac{1}{2} \leq \frac{x^2}{2} \leq 2 \Rightarrow 1 \leq x^2 \leq 4 \\ \therefore & x \in[-2,-1] \cup[1,2]…