Q.

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

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a

[−3,−1]∪[1,2]

b

(−2,−1)∪[2,∞)

c

(−∞,−3⌋∪(−2,−1)∪(2,∞)

d

None of these

answer is C.

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Detailed Solution

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