AP EAMCET · Maths · Functions
For what values of \(x\), the following identity is valid and holds? tan \(\mathrm{h}^{-1}(x)=\frac{1}{2} \log _e\left(\frac{1+x}{1-x}\right)\).
- A \((-\infty, \infty)\)
- B \((1, \infty)\)
- C \((-\infty, 1)\)
- D \((-1,1)\)
Answer & Solution
Correct Answer
(D) \((-1,1)\)
Step-by-step Solution
Detailed explanation
\[ \text \tanh ^{-1} x-\frac{1}{2} \log _e\left(\frac{1+x}{1-x}\right) \] When \(x=1\) identity does not hold as \(\log _e\left(\frac{2}{0}\right)\) will form. At \(x=-1\) also identity does not hold as \(\log _e\left(\frac{0}{-2}\right)\) will form and \(\log _e 0\) does not…
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