JEE Main 2021 (16 Mar, Shift 2) Maths Q64: Monotonicity

Question

Let $f$ be a real valued function, defined on $\mathbf R-\{-1,1\}$ and given by
$f(x)=3\log_e\left|\frac{x-1}{x+1}\right|-\frac{2}{x-1}$.
Then in which of the following intervals, function $f(x)$ is increasing ?

Accepted Answer

Option 2: $(-\infty,-1)\cup\left(\left[\frac12,\infty\right)-\{1\}\right)$

Answer

$(-\infty,\infty)-\{-1,1\}$

Answer

$(-\infty,-1)\cup\left(\left[\frac12,\infty\right)-\{1\}\right)$

Answer

$\left(-\infty,\frac12\right]-\{-1\}$

Answer

$\left(-1,\frac12\right]$

JEE Main 16 March 2021, Shift 2, Maths Q64

Same idea in other shifts