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JEE Main 2006

Exam: JEE Main
Year: 2006
Subject: Mathematics
Chapter: Continuity and Differentiability

JEE Main 2006 · Mathematics · Continuity and Differentiability

The set of points where f(x)=(x)/(1+|x|) is differentiable is

The set of points where

f(x)=\frac{x}{1+|x|}

is differentiable is

Options

A $(-\infty, 0) \cup(0, \infty)$
B $(-\infty,-1) \cup(-1, \infty)$
C $(-\infty, \infty)$
D $(0, \infty)$

Correct answer

C. $(-\infty, \infty)$

Step-by-step solution

f(x)=\left\{

\begin{array}{ll} \frac{x}{1-x}, & x < 0 \\ \frac{x}{1+x}, & x \geq 0 \end{array}

\quad \Rightarrow f^{\prime}(x)= $\begin{cases}\frac{1}{(1-x)^2}, & x < 0 \\ \frac{1}{(1+x)^2}, & x \geq 0\end{cases}$\right.

\therefore f^{\prime}(x)

exist at everywhere.

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