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

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

Text Solution

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Maximum value of `f(x) = sqrt(1^2+(-sqrt3)^2)+1 = 3`
Minimum value of `f(x) = -sqrt(1^2+(-sqrt3)^2)+1 = -1`
So, range of `f(x)` will be `[-1,3].`
As, `f:R->S` is an onto function,
`:.` Interval of `S` will be equal to range of `f(x)`.
`:.` Interval of `S = [-1,3].`
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