TS EAMCET · Maths · Inverse Trigonometric Functions
If for \(|x|>1, \tanh ^{-1}\left(\frac{1}{x}\right)+\operatorname{coth}^{-1}(x)=\log _e(f(x))\), then \(f(-5)=\)
- A \(\frac{3}{2}\)
- B \(\frac{-2}{3}\)
- C \(\frac{2}{3}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{3}\)
Step-by-step Solution
Detailed explanation
Given that, \(\tanh ^{-1}\left(\frac{1}{x}\right)+\operatorname{coth}^{-1} x=\log _e(f(x))\) for \(|x|>1\) \(\because \quad \tanh ^{-1}\left(\frac{1}{x}\right)=\frac{1}{2} \log _e\left(\frac{1+\frac{1}{x}}{1-\frac{1}{x}}\right)\)…
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