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a
(−∞, 0)
b
(−∞, 0]
c
(0, ∞)
d
R−{0}
answer is A.
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Detailed Solution
|x|−x>0⇒x∈(−∞,0) and the domain of sinx is set of all real numbers Since, the domain of sum of two functions is intersection of their domainsTherefore,the domain of the given function is set of all negative real numbers