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

Options

A. `-cos.(y)/(2)`
B. `cos.(y)/(2)`
C. `-2 cos y`
D. `-2 cos y`

Answer

A

Explanation

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)`