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Let f: R to R be defined as f(x)={{:(0...

Let `f: R to R` be defined as
`f(x)={{:(0", x is irrational"),(sin|x|", x is rational"):}`
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 k is an integer

D

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

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