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At how many points is the fucntion f(x)=...

At how many points is the fucntion `f(x)=[x]` discontinuous?

A

1

B

2

C

3

D

Infinite

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `f(x)=[x]`
Let 'c' be any real number.
f is continuous at `x=c" if "L.H.L.=R.H.L=f(c)`
i.e., `underset(xtoc^(-))limf(x)=underset(xtoc^(+))limf(x)=f(c)`
`L.H.L=underset(xtoc^(-))limf(x)=underset(xtoc^(-))lim[x]=c^(-1)`
`R.H.L=underset(xtoc^(+))limf(x)=underset(xtoc^(+))lim[x]=c`
Since, `L.H.LneR.H.L.`
f is discontinous for all `x""inR.`
So, [x] is discontinuous at infinite points.
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