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If f: R->S , defined by f(x)=sinx-sqrt(3...

If `f: R->S ,` defined by `f(x)=sinx-sqrt(3)cosx+1, is onto,` then find the set`Sdot`

Text Solution

Verified by Experts

The correct Answer is:
[-1, 3]
`f(x)=sinx-sqrt(3)cosx+1`
`=2("sin"x(1)/(2)-"cos"(sqrt(3))/(2))+1`
`=2(sinx"cos"(pi)/(3)-cosx"sin"(pi)/(3))+1`
`=2"sin"(x-(pi)/(3))+1`
Clearly, `f` is onto, when the interval of S is `[-1,3].`
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