A) \[(-\infty ,+\infty )\]
B) \[(-\infty ,4]\]
C) \[(4,+\infty )\]
D) \[[-4,4]\]
Correct Answer: B
Solution :
[b] \[\left| \left| x-1 \right|+a \right|=4\Rightarrow \left| x-1 \right|+a=\pm 4\] \[\Rightarrow \left| x-1 \right|=-a\pm 4\] The above equation holds if \[-a+4\ge 0\] or \[-a-4\ge 0\] \[\Rightarrow a\le 4\]or \[a\le -4\Rightarrow a\in (-\infty ,4]\cup (-\infty ,-4]\] \[\Rightarrow a\in (-\infty ,4]\]
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