Domain of definition of the function f(x)=log(|x|−1)⁡x2+4x+4 is

Case I: 0<|x|−1<1 i.e., 1<|x|<2 Then x2+4x+4≤1⇒ x2+4x+3≤0⇒ −3≤x≤−1 So x∈(−2,−1) ∵x2+4x+4>0Case II: |x|−1>1 i.e., |x|>2, then x2+4x+4≥1⇒ x2+4x+3≥0x≥−1 or x≤−3 So, x∈(−∞,−3]∪(2,∞)