Question
The set of real values of $$x$$ satisfying $$\left| {\left| {x - 1} \right| - 1} \right| \leqslant 1$$ is
A.
$$\left[ { - 1,3} \right]$$
B.
$$\left[ {0,2} \right]$$
C.
$$\left[ { - 1,1} \right]$$
D.
None of these
Answer :
$$\left[ { - 1,3} \right]$$
Solution :
$$\eqalign{
& \left| {\left| {x - 1} \right| - 1} \right| \leqslant 1 \cr
& \Rightarrow \,\,0 \leqslant \left| {x - 1} \right| \leqslant 2 \cr
& \Rightarrow \,\,\left| {x - 1} \right| \leqslant 2 \cr
& \Rightarrow \,\, - 1 \leqslant x \leqslant 3. \cr} $$