AP EAMCET · Maths · Functions
The domain of the real valued function
\(f(x)=\sqrt{\frac{2-|x|}{3-|x|}}\) is
- A \((-\infty, \infty)\)
- B \((-\infty,-3) \cup(2, \infty)\)
- C \((-\infty,-3] \cup(-2,2) \cup[3, \infty)\)
- D \((-\infty,-3) \cup[-2,2] \cup(3, \infty)\)
Answer & Solution
Correct Answer
(D) \((-\infty,-3) \cup[-2,2] \cup(3, \infty)\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=\sqrt{\frac{2-|x|}{3-|x|}}\) For \(f(x)\) to be defined, \(\frac{2-|x|}{3-|x|} \geq 0\) Case I If \(x \geq 0\), then \(\frac{2-x}{3-x} \geq 0 \Rightarrow \frac{x-2}{x-3} \geq 0\) Thus, \(x \in(-\infty, 2] \cup(3, \infty)\)...(i) Case II If \(x Thus,…
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