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Let f:RrarrR be defined as . f(x)={(0, "...

Let `f:RrarrR` be defined as .
`f(x)={(0, "x is irrational"),(sin|x|,"x is irrational"):}` Then which of the following is true?

A

f is discontinuous for all x

B

f is continuous for all x

C

f is discontinuous at `x=kpi`, where kis an integer

D

f is continuous at `x=kpi`, where kis an integer

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The correct Answer is:
D
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