Find the interval for which the function $f(x) = \cot^{-1}x + x$ increases.

$(-\infty, \infty)$

The correct answer is Option (3) → $(-\infty, \infty)$ ##

Given, $f(x) = \cot^{-1}x + x$

$f'(x) = \frac{-1}{1+x^2} + 1 = \frac{-1+1+x^2}{1+x^2}$

$= \frac{x^2}{1+x^2} \geq 0$ for all $x \in \mathbb{R}$.

$∴f$ increases for $(-\infty, \infty)$.