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Let `f:[-(pi)/(3),(2pi)/(3)]rarr[0,4]` be a function defined as `f(x) as f(x) = sqrt(3)sin x -cos +2`. Then `f^(-1)(x)` is given byA. `sin^(-1),((x-2)/(2))-(pi)/(6)`B. `sin^(-1)((x-2)/(2))+(pi)/(6)`C. `sin^(-1)((x+2)/(2))-(pi)/(6)`D. `(2pi)/(3)+cos^(-1)((x-2)/(3))` |
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Answer» Correct Answer - B `f (x) =sqrt(3)sin x-cos x+2=2sin (x-(pi)/(6))+2` Since f (x) is one -one and onto, f is invertible. `implies f^(-1)(x)=sin^(-1)((x)/(2)-1)+(pi)/(6). |(pi)/(2)-1|le 1` Because for all `x [0,4]` Also using `sin^(-1) alpha+cos^(-1) alpha=(pi)/(2)` `f^(-1)(x) =(pi)/(2) -cos^(-1) ((x-2)/(2))+(pi)/(6)` `(2pi)/(3)-cos^(-1)((x-2)/(3))` |
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