Q. The function $f(x) = \frac{x}{1 + |x|}$ is
A) Strictly increasing
B) Strictly decreasing
C) Neither increasing nor decreasing
D) Not differential at $x = 0$
Explanation
(a)
Given, $f(x) = \frac{x}{1 + |x|}$
$\therefore\ \ \ f^{'}(x) = \frac{\left( 1 + |x| \right).1 - x.\frac{|x|}{x}}{\left( 1 + |x| \right)^{2}}$
$= \frac{1}{\left( 1 + |x| \right)^{2}} > 0\forall\ x \in R$
$\Rightarrow \ \ \ f(x)$ is strictly increasing
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.