Question

The domain of definition of the function `f(x)=sqrt(sin^(-1)(2x)+pi/6)` for real-valued `x` is
A. `[-(1)/(4),(1)/(2)]`
B. `[-(1)/(2),(1)/(2)]`
C. `(-(1)/(2),(1)/(9))`
D. `[-(1)/(4),(1)/(4)]`

Answer 1

Correct Answer - A
Here, `f(x)=sqrt(sin^(-1)(2x)+(pi)/(6))`, to find domain we must have,
`sin^(-1)(2x)+(pi)/(6) ge 0 " "["but "-(pi)/(2) le sin^(-1)theta le (pi)/(2)]`
` -(pi)/(6) le sin^(-1) (2x) le (pi)/(2)`
`sin(-(pi)/(6)) le 2x le "sin"(pi)/(2) rArr (-1)/(2) le 2x le (1)/(2)`
`(-1)/(4) le x le (1)/(2)`
`because x in [(-1)/(4), (1)/(2)]`