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TS EAMCET · Maths · Functions

If the domain of the real valued function \(f(x)=\frac{1}{\sqrt{\log _{\frac{1}{3}}\left(\frac{x-1}{2-x}\right)}}\) is \((a, b)\), then \(2 b=\)

  1. A \(a-1\)
  2. B \(a\)
  3. C \(a+1\)
  4. D \(a+2\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(a+2\)

Step-by-step Solution

Detailed explanation

\(\frac{x-1}{2-x} > 0 \Rightarrow (x-1)(2-x) > 0 \Rightarrow (x-1)(x-2) \(\log _{\frac{1}{3}}\left(\frac{x-1}{2-x}\right) > 0 \Rightarrow \frac{x-1}{2-x} \((2x-3)(2-x) 0 \Rightarrow x 2\) Combining conditions: \((1 2) \Rightarrow 1 Domain is…