If x in[-1,(-1)/(sqrt(2))], then the inv...

If `x in[-1,(-1)/(sqrt(2))]`, then the inverse of the function `f(x)=sin^(-1)(2x sqrt(1-x^(2)))` is given by

A

`-cos.(y)/(2)`

B

`cos.(y)/(2)`

C

`-2 cos y`

D

`-2 cos y`

Verified by Experts

The correct Answer is:

A

For `x in [-1,(-1)/(sqrt(2))]`,
`y=-pi-2sin^(-1)x`
`rArr sin^(-1)x=(-pi)/(2)-(y)/(2)`
`rArr f^(-1)(y)=-sin((pi)/(2)+(y)/(2))=-cos.(y)/(2)`

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