1.

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]`

Answer» Correct Answer - `[-1//4,1//2]`
We have `f(x)=sqrt(sin^(-1)(2x)+(pi)/(6))`
We must have `sin^(-1)(2x) +(pi)/(6) ge 0`
`implies sin^(-1)(2x) ge -(pi)/(6) " …(1) " `
But `-(pi)/(2) le sin^(-1)(2x) le (pi)/(2) " (2)" `
From (1) and (2), we have
` -(pi)/(2) le sin^(-1) (2x) le (pi)/(2)`
`implies "sin"(-(pi)/(6)) le 2x le "sin"(pi)/(2)`
`implies -(1)/(2) le 2x le 1`
`implies -(1)/(4) le x le (1)/(2)`
Hence, domain is `[-(1)/(4),(1)/(2)]`


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