The range of the function `f` defined by `f(x)=[1/(sin{x})]` (where [.] and `{dot},` respectively, denote the greatest integer and the fractional part functions) is I, the set of integers N, the set of natural number W, the set of whole numbers {1,2,3,4,...}

Options

A. `Z `
B. `N`
C. `{ x : x ge 0 , x in Z}`
D. `{x : x ge 2, x in N }`

Answer

B

Explanation

We know that
`0 lt {x} lt 1 " ""for all " x in R-Z`
`rArr 0 lt sin {x} lt sin 1 " ""for all" x in R- Z`
`rArr 0 lt sin {x} lt 0.841"for all" x in R-Z " "[because sin 1= 0.8414]`
`rArr (1)/(sin{x}) lt 1.1883 " ""for all" x in R-Z`
`rArr [(1)/(sin{x})] ge 1 " ""for all" x in R - Z`
`rArr f(x) ge1 " ""for all " x in R-Z`
Range of `f(x) = N`.