InterviewSolution
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InterviewSolution
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The largest interval lying in `(-pi/2,pi/2)`for which thefunction `[f(x)=4^-x^2+cos^(-1)(x/2-1)+log(cosx)]`is defined,is(1) `[0,pi]`(2) `(-pi/2,pi/2)`(3) `[-pi/4,pi/2)`(4) `[0,pi/2)`A. `[- pi//4, 2)`B. `[ 0, pi//2)`C. `[0, pi]`D. ` (-pi//2, pi//2)` |
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Answer» Correct Answer - B Clearly, `4^(-x^(2))` is defined for all `x in R` and `cos^(-1)((x)/(2)-1)` is defined for `-1 le (x)/(2) - 1 le 1` i.e., for `0 le (x)/(2) le 2` or, `x in [0,4]` Also ,log cos x is defined for all `x in (-pi//2,pi//2)` `therefore f(x)` is defined for all `x in (-(pi)/(2),(pi)/(2)) nn[0,4]nnR = [0,(pi)/(2))` |
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