Functions
Inverse Functions
JEE Main 2020
Grade 12
Question:
The inverse of $f(x) = \frac{8^{2x} - 8^{-2x}}{8^{2x} + 8^{-2x}}$, $x \in (-1, 1)$, is:
(1) $\frac{1}{4} \log_8 \frac{1 - x}{1 + x}$
(2) $\frac{1}{4} \log_8 \frac{1 + x}{1 - x}$
(3) $\frac{1}{2} \log_8 \frac{1 + x}{1 - x}$
(4) $\frac{1}{2} \log_8 \frac{1 - x}{1 + x}$
Step-by-Step Solution
Key Concept: Let $t = 8^{4x}$. Write $y = (t - 1)/(t + 1)$, cross-multiply and solve for $t$, then take $\log_8$ to find $x$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)