InterviewSolution
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InterviewSolution
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The set of real values of x satisfying `||x-1|-1|le 1`, isA. `[-1, 3]`B. `[0, 2]`C. `[-1, 1]`D. none of these |
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Answer» Correct Answer - A Since x-1 changes its sign as x passes through 1. So, following cases arise. CASE I When `x lt 1` In this case, we have `|x-1|= -(x-1)` `therefore ||x-1|-1| le1` `rArr |-(x-1)-1| le 1` `rArr |-x| le1` `rArr |x| le 1` `rArr -1 le x le 1 " "[because |x| le a hArr -a le x le a]` `rArr -1 le x lt 1 " " [because x lt 1]` `therefore x in [-1, 1])` CASE II When `x ge 1` In this case, we have |x-1| = x -1 `therefore ||x-1|-1| le 1` `rArr |x-1-1| le 1` `rArr |x-2| le 1 rArr 2-1 le x le 2 + 1 rArr x in [1, 3]` Hence, `x in [-1, 3]` |
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