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Question

The domain of the function
f(x)=x1+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)=x1+2(x+4)0.52(x+6)0.5+(x+5)0.5+4(x+10)0.5f(x)=x1+2x+42(x+6)+x+5+4x+10

For the function to be defined
x+4>0, x+60, x+50, x+10>0, 2x+60
From the above conditions, we get
x>4, x+62x>4, x2
Hence, the required domain is
(4,){2}

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