AP EAMCET · Maths · Functions
The domain of the function \(f(x)=\sqrt{\log _e\left(\frac{1}{x^2-4 x+4}\right)}+\sin ^{-1}\left(x^2-2\right)\) is
- A \([1,3]\)
- B \([1,3)\)
- C \([1, \sqrt{3}]\)
- D \([1, \sqrt{3})\)
Answer & Solution
Correct Answer
(C) \([1, \sqrt{3}]\)
Step-by-step Solution
Detailed explanation
\(x^2-4x+4 = (x-2)^2\) For \(\sqrt{\log _e\left(\frac{1}{(x-2)^2}\right)}\): \(\frac{1}{(x-2)^2} > 0 \implies x \ne 2\) \(\log _e\left(\frac{1}{(x-2)^2}\right) \ge 0 \implies \log _e((x-2)^{-2}) \ge 0\) \(-2 \log _e(|x-2|) \ge 0 \implies \log _e(|x-2|) \le 0\) \(0…
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