Q. The function $f(x) = \cot^{- 1}{x + x}$ increasing in the interval
A) $(1,\ \infty)$
B) $( - 1,\ \infty)$
C) $( - \infty,\ \infty)$
D) $(0,\ \infty)$
Explanation
(c)
$f(x) = \cot^{- 1}{x + x}$
$\Rightarrow f^{'}(x) = - \frac{1}{1 + x^{2}} + 1$
$= \frac{x^{2}}{1 + x^{2}},\ clearly,\ f’(x) >$for all$x$.
So, $f(x)$ increases in ($- \infty,\infty$).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.