Functions
Properties of Logarithmic Functions
JEE Main 2019
Grade 12
Question:
If $f(x) = \log_e\frac{1 - x}{1 + x}$, $|x| < 1$, then $f\left(\frac{2x}{1 + x^2}\right)$ equals:
(1) $-2f(x)$
(2) $2f(x)$
(3) $[f(x)]^2$
(4) $-f(x)$
Step-by-Step Solution
Key Concept: Write $\frac{2x}{1 + x^2}$ inside the log formula and simplify the fraction $\frac{1 - 2x/(1 + x^2)}{1 + 2x/(1 + x^2)}$. Recognise the result as a power of $f(x)$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)