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The function f(x)=(sec^(-1)x)/(sqrt(x-[x...

The function `f(x)=(sec^(-1)x)/(sqrt(x-[x]),` where `[x]` denotes the greatest integer less than or equal to `x ,` is defined for all `x in ` (a) `R` (b) `R-{(-1,1)uu{n"|"n in Z}}` (c) `R-(0,1)` (d) `R-{n|n in N}`

A

R

B

`R-{(-1,1) cup {n|n in Z}}`

C

`R^(+) -(0,1)`

D

`R^(+) -{n|n in N}`

Text Solution

Verified by Experts

The correct Answer is:
B
The function `sec^(-1)x` is defined for all `x in R - (-1,1)`
and the function `(1)/(sqrt(x-[x]))` is defined for all ` x in R-Z.`
So, the given function is defined for all ` x in R -{(-1,1) cup {n |n in Z}}.`
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