InterviewSolution
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InterviewSolution
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If `f:[-pi//2,pi//2] cupR` given by `f(x)=cosx+sin[(x+1)/(lambda)]` is an even function. Then the set of values of ` lambda(lambda gt0)` is Here, `[*]` denotes the greatest integer function.A. `((-pi)/(2),(pi)/(2))`-{0}B. `((pi+2)/(2),oo)`C. `(0,(pi+2)/(2)) cup ((pi+2)/(2),oo)`D. `((-pi)/(2),(pi+2)/(2))-{0}` |
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Answer» Correct Answer - B For `f(x)` to be even , we must have ` sin[(x+1)/(lambda)]=0` `implies [(x+1)/(lambda)]=0` `implies o le (x+1)/(lambda) lt 1 implies 0 le x +1 lt lambdaimplies x+1 gt0 and lambda gt x+1`. Now , `x in [-(pi)/(2),(pi)/(2)]implies -(pi)/(2) +1 le x+1 le(pi)/(2)+1` Therefore , for `x+1 ge0` , we must have `0 le x +1 le (pi)/(2) +1 implies ` maximum value of `x+1` is `(pi)/(2)+1` . Now, `lambda gt x+1 implies lambda gt ` maximum value of `x+1 implies lambda gt pi//2+1` Hence , `lambda in ((pi)/(2)+1,oo)` |
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