AP EAMCET · Maths · Functions
For \(f(x)=\sin \left(\frac{1}{|x| \sqrt{x^2-1}}\right)\) the domain and range of \(f(x)\) in \(R\) are
- A \(R-\{0, \pm 1\}\) and \([-1,1]\), respectively
- B \(R-[-1,1]\) and \([-1,1]\) respectively
- C \(R-\{0, \pm 1\}\) and \([0,1]\), respectively
- D \(R-[-1,1]\) and \([0,1]\), respectively
Answer & Solution
Correct Answer
(B) \(R-[-1,1]\) and \([-1,1]\) respectively
Step-by-step Solution
Detailed explanation
Given function \(f(x)=\sin \left(\frac{1}{|x| \sqrt{x^2-1}}\right)\) For the domain, \(|x| \neq 0 \Rightarrow x \neq 0\) and \(x^2-1>0 \Rightarrow x \in \mathbf{R}-[-1,1]\) So domain of \(f\) is \(R-[-1,1]\) and we know the range of sine function is \([-1,1]\).
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