The domain of definition of the function `f(x)=sqrt(sin^(-1)(2x)+pi/6)` for real-valued `x` is `[-1/4,1/2]` (b) `[-1/2,1/2]` (c) `(-1/2,1/9)` (d) `[-1/4,1/4]`

Options

A. `[-1//4, 1//2]`
B. `[-f 1//2, 1//2]`
C. `[-1//2, 1//9]`
D. `[-1//4, 1//4]`

Answer

A

Explanation

f(x) is defined, if
`-1 le 2x le 1 and sin^(-1) 2x +(pi)/(6) ge 0`
`rArr x in [-1//2,1//2] and sin^(-1)2x ge -(pi)/(6)`
`rArr x in [-1//2,1//2] and 2x ge sin ((pi)/(6))" ["because"Since is incresing on"[-pi//2,pi//2]]`
`rArr x in [-1//4,1//2] and x ge - 1//4`
`rArr x in [-1//4,1//2]`