The set of point, where $f(x)=\frac{x}{1+|x|}$ is differentiable is
34 views
0 Votes
0 Votes

The set of point, where $f(x)=\frac{x}{1+|x|}$ is differentiable is

(A) $(-\infty, 0) \cup(0, \infty)$

(B) $(-\infty,-1) \cup(-1, \infty)$

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

(D) $(0, \infty)$

1 Answer

0 Votes
0 Votes
 
Best answer

SOLUTION —

$f(x)=\left\{\begin{array}{ll}x /(1-x), & x<0 \\ x /(1+x), & x \geq 0\end{array}\right.$

$\Rightarrow f^{\prime}(x)=\left\{\begin{array}{ll}1 /(1-x)^2, & x<0 \\ 1 /(1+x)^2, & x \geq 0\end{array}\right.$

Hence, $f(x)$ exist every where

So, The correct option will be (C).

RELATED DOUBTS

1 Answer
0 Votes
0 Votes
30 Views
1 Answer
0 Votes
0 Votes
67 Views
1 Answer
0 Votes
0 Votes
53 Views
1 Answer
0 Votes
0 Votes
58 Views
1 Answer
0 Votes
0 Votes
72 Views
1 Answer
0 Votes
0 Votes
54 Views
1 Answer
0 Votes
0 Votes
55 Views
1 Answer
0 Votes
0 Votes
45 Views
1 Answer
0 Votes
0 Votes
50 Views
1 Answer
0 Votes
0 Votes
48 Views
1 Answer
0 Votes
0 Votes
59 Views
1 Answer
0 Votes
0 Votes
51 Views
Peddia is an Online Question and Answer Website, That Helps You To Prepare India's All States Boards & Competitive Exams Like IIT-JEE, NEET, AIIMS, AIPMT, SSC, BANKING, BSEB, UP Board, RBSE, HPBOSE, MPBSE, CBSE & Other General Exams.
If You Have Any Query/Suggestion Regarding This Website or Post, Please Contact Us On : [email protected]

CATEGORIES