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

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1.	If `f:R->S` defined by `f(x)=sinx-sqrt(3)cosx+1` is onto , then the interval of S is :A. [0,1]B. [-1,1]C. [0,3]D. [-1,3]
Answer» Correct Answer - D We have `sqrt(1+(sqrt(3))^(2)) le sin x sqrt3 cos x le sqrt(1+(sqrt3)^(2))"for all "x in R` `Rightarrow -2 le sin x-sqrt3 cos x le 2" ""for all "x in R` `Rightarrow -1 le sin x-sqrt3 cos x+1 le 3" ""for all "x in R` `Rightarrow -1 le f(x)" "le sqrt3" ""for all "x in R` `Rightarrow "Range(f)"=[-1,3]` If `f:R to S` is onto, then S=Range(f)=[-1,3]

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