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Let f:A->R, where A=R\ {0} is such that...

Let `f:A->R`, where `A=R\ {0}` is such that `f(x)=(x+|x|)/x` On which one of the following sets is f(x) continuous?

A

A

B

`B={x""inR:xge0}`

C

`C={x""inR:xle0}`

D

D=R

Text Solution

Verified by Experts

The correct Answer is:
A
For `xge0`
`f(x)=(x+x)/(x)=2`
For `xlt0`
`f(x)=(x-x)/(x)=1`
`underset(xto0^(+))limf(x)=2`
`underset(xto0^(-))limf(x)=0`
f(0)=2
`implies` It is discontinuons at x=0.
Option (a) is correct.
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