Question

The function $f(x) = cot^{-1}x + x$ increases in the interval

• A. $\left(1, \infty \right)$
• B. $\left(-1, \infty \right)$
• C. $\left(0, \infty \right)$
• D. $\left(-\infty, \infty \right)$

Answer 1

Answer: (D)

$f\left(x\right) = cot^{-1}x + x$
$\Rightarrow f'\left(x\right) = \frac{-1}{1+x^{2}} + 1$
$\Rightarrow f'\left(x\right) = \frac{x^{2}}{1+x^{2}} \ge 0$,
for $x \in R$
$\therefore f\left(x\right)$ is increasing on $\left(-\infty, \infty\right)$.