What is the range of -abs(x-1)+2?

Jun 11, 2015

We first look at $| x - 1 |$ which is allways $\ge 0$
So the negative is allways $\le 0$
$\to - | x - 1 | \le 0 \to - | x - 1 | + 2 \le 2$
Since there is no upper limit to $| x - 1 |$, there is no lower limit to the equation as a whole, or:
$- \infty < - | x - 1 | + 2 \le 2$