AP EAMCET · Maths · Functions
Domain of the real valued function \(f(x)=\log \left(x^2-1\right)+x \operatorname{coth}^{-1} x\) is
- A \(\mathbb{R}\)
- B \((-1,1)\)
- C \(\mathbb{R}-[-1,1]\)
- D \(\mathbb{R}-[0,1]\)
Answer & Solution
Correct Answer
(C) \(\mathbb{R}-[-1,1]\)
Step-by-step Solution
Detailed explanation
For \(\log \left(x^2-1\right)\): \(x^2-1 > 0 \implies (x-1)(x+1) > 0 \implies x \in (-\infty, -1) \cup (1, \infty)\) For \(\operatorname{coth}^{-1} x\): \(|x| > 1 \implies x \in (-\infty, -1) \cup (1, \infty)\) The domain of \(f(x)\) is the intersection:…
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