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The set of points where f(x)=x/(1+|x|) i...

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

A

`(-oo, -1) cup (-1, oo)`

B

`(-oo, oo)`

C

`(0, oo)`

D

`(-oo, 0) cup (0, oo)`

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)=(x)/(1+|x|)`
`rArr f(x)={((x)/(1-x)",",x lt 0),((x)/(1+x)",",x ge 0):}`
`rArr f.(x)={((x)/((1-x)^(2))",", x lt 0),((x)/((1+x)^(2))",", x gt 0):}`
Here we observe that
`LHD=1=Lf.(0)`
`RHD=1=Rf.(0)`
`:.` Function is differentiable over `(-oo, oo)`
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