The domain of definition of the function f(x)=x⋅1+2(x+4)−0.52−(x+6)0.5+(x+5)0.5+4(x+10)−0.5 is
A
(−4,∞)−{2}
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B
(−4,∞)−{−2}
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C
R−(−4,0)
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D
(0,∞)
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Solution
The correct option is B(−4,∞)−{−2} f(x)=x⋅1+2(x+4)−0.52−(x+6)0.5+(x+5)0.5+4(x+10)−0.5 f(x)=x⋅1+2√x+42−√(x+6)+√x+5+4√x+10 for the function to be defined x+4>0,x+6≥0,x+5≥0,x+10>0,2−√x+6≠0⇒x>−4,√x+6≠2⇒x>−4,x≠−2 Hence required domain is (−4,∞)−{−2}