Domain of f is defined, if |[|x|−1]|−5>0 ⇒|[|x|−1]|>5 ⇒ either [|x|−1]<−5 or [|x|−1]>5 Case I [|x|−1]<−5 ⇒|x|−1<−5 ⇒|x|<−4, which is not possible. Case II [|x|−1]>5 ⇒|x|−1≥6 ⇒|x|≥7 ∴x∈(−∞,−7)∪[7,∞)