The domain of definition of the function f(x)=1√|[∥x∥−1]|−5 is
f(x)=1√|[|x|−1|]|−5
For the function to be defined
|[|x|−1]|−5>0⇒|[|x|−1]|>5⇒−5>[|x|−1]>5⇒−5>|x|−1≥6
⇒−4>|x|≥7
−4>|x| is not possible
⇒|x|≥7
⇒−7≥x≥7
⇒x∈(−∞,−7]∪[7,∞)
Hence, option A is correct.