The range of function `f(x)=sin^(-1)(x-sqrt(x))` is equal to

Options

A. `["sin"^(-1)(1)/(4),(pi)/(2)]`
B. `["sin"^(-1),(pi)/(2)]`
C. `[-"sin"^(-1)(1)/(4),(pi)/(2)]`
D. `[-"sin"^(-1)(1)/(2),(pi)/(2)]`

Answer

C

Explanation

We have `f(x)=sin^(-1)(x-sqrt(x))`
`=sin^(-1)((sqrt(x)-(1)/(2))^(2)-(1)/(4))`
`therefore` Range of f(x) is `[sin^(-1)((-1)/(4)), sin^(-1)1]`
`=[-sin^(-1)(1)/(4),(pi)/(2)]`