Question

The set of real values of $x$ satisfying ||$x-1|-1|\mid \le 1$ is

• A. [-1,3]
• B. [0,2]
• C. [-1,1]
• D. None of these

Answer 1

Answer: (A)

||$x-1|-1|\le 1$
$\Rightarrow -1\le |x-1|-1\le 1$
$\Rightarrow 0\le |x-1|\le 2$
$\Rightarrow -2\le x-1\le 2$
$\Rightarrow -1\le x\le 3$
$\Rightarrow x\in [-1,3]$