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

Case I: $$0$$ $$0Case$$ 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$$,∞$$)

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

Correct option is 3(−∞,−3⌋∪(−2,−1)∪(2,∞)

Questions

Domain of definition of the function $f (x) = \sqrt{\log_{(| x | - 1)} (x^{2} + 4 x + 4)} is$

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[−3,−1]∪[1,2]

(−2,−1)∪[2,∞)

(−∞,−3⌋∪(−2,−1)∪(2,∞)

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detailed solution

Correct option is C

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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