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The domain of the function f(x)=sqrt(log...

The domain of the function `f(x)=sqrt(log(1/(|sinx|)))` `R-{-pi,pi}` (b) `R-{npi|npiZ}` `R-{2npi|n in z}` (d) `(-oo,oo)`

A

`R-{-pi,pi}`

B

`R-{n pi|n in Z}`

C

`R-{2n pi|n in z}`

D

`(-oo,oo)`

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)` is defined for
`log ((1)/(|sinx|)) ge 0`
or `(1)/(|sinx|) ge 1 " and " |sinx| ne 0`
or ` |sinx| ne 0 " "[ :' (1)/(|sinx|) ge 1 " for all "x]`
or `x ne n pi, n in Z`
Hence, the domain of `f(x)` is `R-{n pi: n in Z}.`
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