JEE PYQ: Functions Question 21
Question 21 - 2020 (08 Jan Shift 1)
The inverse function of $f(x) = \frac{8^{2x} - 8^{-2x}}{8^{2x} + 8^{-2x}}$, $x \in (-1, 1)$, is:
(1) $\frac{1}{4} \log_e \left(\frac{1+x}{1-x}\right)$
(2) $\frac{1}{4} (\log_8 e) \log_e \left(\frac{1-x}{1+x}\right)$
(3) $\frac{1}{4} \log_e \left(\frac{1-x}{1+x}\right)$
(4) $\frac{1}{4} (\log_8 e) \log_e \left(\frac{1+x}{1-x}\right)$
Type: MCQ
Show Answer
Answer: (1) $\frac{1}{4} \log_e \left(\frac{1+x}{1-x}\right)$
Solution
$8^{4x} = \frac{1+y}{1-y}$
$f^{-1}(x) = \frac{1}{4} \log_8\left(\frac{1+x}{1-x}\right)$
BETA
