For x ∈ R, find all possible values of $|x-3|-2$

$[-2,∞)$ $(-∞,∞)$ $[0,∞)$ $[∞,1)$

$[-2,∞)$

We know that $|x-3|≥0\,∀\,x∈R$ $⇒|x-3|-2≥-2$ $⇒|x-3|-2∈[-2,∞)$