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The range of function f(x)=sin^(-1)(x-sq...

The range of function `f(x)=sin^(-1)(x-sqrt(x))` is equal to

A

`["sin"^(-1)(1)/(4),(pi)/(2)]`

B

`["sin"^(-1),(pi)/(2)]`

C

`[-"sin"^(-1)(1)/(4),(pi)/(2)]`

D

`[-"sin"^(-1)(1)/(2),(pi)/(2)]`

Text Solution

Verified by Experts

The correct Answer is:
C
We have `f(x)=sin^(-1)(x-sqrt(x))`
`=sin^(-1)((sqrt(x)-(1)/(2))^(2)-(1)/(4))`
`therefore` Range of f(x) is `[sin^(-1)((-1)/(4)), sin^(-1)1]`
`=[-sin^(-1)(1)/(4),(pi)/(2)]`
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