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The number of integral values in the range of the function `f(x)=sin^(-1)x-cot^(-1)x+x^(2)+2x +6` isA. 10B. 11C. 12D. 8 |
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Answer» Correct Answer - D `f(x)=sin^(-1)x-((pi)/(2)-tan^(-1)x)+(x+1)^(2)+5` `=sin^(-1)x + tan^(-1)x-(pi)/(2)+(x +1)^(2)+5` Domain of f(x) is [-1,1] and `sin^(-1) x, tan^(-1)x` and `(x+1)^(2)` are all increasing in [-1,1] `therefore f(x)` is increasing `f(-1)=(-5pi)/(4)+5` and `f(1)=(pi)/(4)+9` `therefore` Range of f(x) is `[(-5pi)/(4)+5,(pi)/(4)+9]` |
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