The domain of definiton of the function ` f(x) = cot^(-1) {(x)/(sqrt(x^(2)-[x^(2)]))}` is

Options

A. `R - {pm sqrtn : n in N }`
B. `R - { pm sqrtn : n ge 0, ne Z)`
C. `R`
D. `R-{0}`

Answer

B

Explanation

We know that `cos^(-1) x` is defined for all `x in R` .
Therefore, `cot^(-1){(x)/(sqrt(x^(2) -[x]))}` is defined, if
`x^(2) -[x^(2)] gt0`
`rArr x^(2) gt [x^(2)]`
`rArr x^(2) in R and x^(2) ne 0,1,2,3,....`
`rArr x ne R and x ne p, sqrt(n),n=0,1,2,.....`
`rArr x in R- {pm sqrt(n) : ngt 0, n in z}`
Hence, domina `f = R -{pm sqrt(n) :n gt 0, n in Z}`