Question

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 ` `R` (b) `R-{(-1,1)uu{n"|"n in Z}}` `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}`

Answer 1

Correct Answer - 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}}.`