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The domain of the real valued function ...

The domain of the real valued function
`f(x)=sqrt(1-2x)+2sin^(-1)((3x-1)/(2))` is

A

`[-(1)/(3),1]`

B

`[(1)/(2),1]`

C

`[-(1)/(2),(1)/(3)]`

D

`[-(1)/(3),(1)/(2)]`

Text Solution

Verified by Experts

The correct Answer is:
D
Since, the given function is
`f(x)=sqrt(1-2x)+2sin^(-1)((3x-1)/(2))`.
For domain of f(x), `1-2xge0" and "-1le (3x-1)/(2)le1`
`implies" "xle(1)/(2)" and "-2le3x-1le2`
`implies" "xle(1)/(2)" and "-(1)/(3)lexle1`
`:." Domain of "f(x)=[-(1)/(3),(1)/(2)]`
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