InterviewSolution
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InterviewSolution
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Find the set of all solutions of the equation `2^|y| -|2^(y -1) -1| = 2^(y -1) +1 ` |
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Answer» Correct Answer - `y in{-1}uu[1,oo)` Given, ` 2^(|y|)-|2^(y-1)-1|=2^(y-1)+1` Case I When `y in (-oo, 0]` `therefore 2^(-y)+(2^(y-1)-1)2^(y-1)+1` `implies 2^(-y)=2` `impliesy=-1 in (-oo,0]" "...(i)` Case II When `y in (0,1]` `therefore2^(y)+(2^(y-1)-1)=2^(y-1)+1` `implies 2^(y)=2` `impliesy=1 in (0,1] " "...(ii)` Case III When `y in (1, oo)` `therefore2^(y)-2^(y-1)+1=2^(y-1)+1` `implies 2^(y)-2.2^(y-1)=0` implies 2^(y)-2^(y)=0 "true for all" y gt 1 " "...(iii)` From Eqs. (i), (ii), (iii), we get `y in{-1}uu[1,oo).` |
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