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. I, the set of integers
B. N, the set of natural numbers
C. W, the set of whole numbers
D. `{1,2,3,4,…}`

Answer

D

Explanation

Since `{x} in [0,1), sin {x} in (0,sin 1)` as `f(x)` is defined if ` sin{x} ne 0,` i.e.,
`(1)/(sin{x}) in ((1)/(sin1),oo) " or " [(1)/(sin{x})] in {1,2,3,... }`
Note that ` 1 lt (pi)/(3) " or " sin 1 lt "sin"(pi)/(3)=0.866 " or " (1)/(sin 1) gt 1.155.`