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Question

Let f be a real valued function, defined on R{1,1} and given by f(x)=3logex1x+12x1. Then in which of the following intervals, function f(x) is increasing ?

A
(,1)([12,){1})
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B
(1,12]
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C
(,){1,1}
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D
(,12]{1}
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Solution

The correct option is A (,1)([12,){1})
f(x)=3logex1x+12x1
f(x)=3(x+1x1×x+1(x1)(x+1)2)+2(x1)2
=6(x1)(x+1)+2(x1)2
=4(2x1)(x+1)(x1)2


x(,1)[12,){1}

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