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Let f(x) be defined as follows : f(x)=...

Let f(x) be defined as follows :
`f(x)={{:(2x+1",",-3ltxlt-2),(x-1",",-2lexlt0),(x+2",",0lexlt1):}`
Which one of the following statements is correct in respect of the above function?

A

It is discontinuous at x=-2 but continuous at every other point.

B

It is continuous only in the interval (-3,-2).

C

It is discontinuous at x=0 but continuous at every other point.

D

It is discontinuous at every point.

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)={{:(2x+1",",-3ltxlt-2),(x-1",",-2lexlt0),(x+2",",0lexlt1):}`
Here, `f(0^(-))=-1andf(0^(+))=2`
So, f(x) is discontinuons at x=0 and continuous at other points.
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