If f(x)=[x](sin kx)^(p) is continuous fo...

If `f(x)=[x](sin kx)^(p)` is continuous for real x, then (where [.] represents the greatest integer function)

A

`k in [npi, n in I], p gt 0`

B

`k in {2npi, n in I}, p gt0`

C

`k in {npi, n in I}, p in R-{0}`

D

`k in {npi, n I, n ne 0}, p in R-{0}`

Text Solution

Verified by Experts

The correct Answer is:

A

`f(x)=[x](sin kx)^(p)`
`(sin kx)^(p)` is continuous function `AA x in R, k in R` and `p gt0.[x]` is discontinuous at `x in I`
For `k=npi, n in I`
`f(x)=[x](sin(n pix))^(p)`
`underset(xrarra)(lim)f(x)=0, a in I`
and f(a) = 0
So, f(x) becomes continuous for all `x in R`

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