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Let f(x)={{:(8^((1)/(x))",",xlt0,),(a[x]...

Let `f(x)={{:(8^((1)/(x))",",xlt0,),(a[x]",",a inR-{0}",",xge0):}` (where [.] denotes the greatest integer function).
Then f(x) is

A

continuous only at a finite number of points.

B

discontinuous at a finite number of points.

C

discontinuous at an infinite number of points.

D

discontinuous at x = 0.

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(xrarr0^(-))(lim)f(x)=underset(hrarr0)(lim)8^(-(1)/(h))=0" (where h gt 0)"`
`underset(xrarr0^(+))(lim)f(x)=underset(xrarr0^(+))(lim)a[x]=a(0)=0`
`therefore" f(x) is continuous at x = 0"`.
At positive integral points, f(x) is not continuous.
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