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$The domain of the function f (x) = \log_{3 + x} (x^{2} - 1) is$

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(−3,−1)∪(1,∞)

[−3,−1)∪[1,∞)

(−3,−2)∪(−2,−1)∪(1,∞)

[−3,−2)∪(−2,−1)∪[1,∞)

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detailed solution

Correct option is C

f(x) is to be defined when x2−1>0 and 3+x>0 and 3+x≠1 , i.e., x2>1 and x>−3 and x≠−2 i.e., x<−1 or x>1 and x>−3 and x≠−2∴ Df=(−3,−2)∪(−2,−1)∪(1,∞)

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The domain of the function f(x)=log3+x⁡x2−1 is

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$The domain of the function f (x) = \log_{3 + x} (x^{2} - 1) is$