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Question

The true set of real value of x for which the function, f(x)=x ln xx+1 is positive is

A
(1, )
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B
(1/e, )
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C
(e, )
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D
(0, 1)(1, )
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Solution

The correct option is D (0, 1)(1, )
f(x)=xlnxx+1f(1)=0

On differentiating w.r.t x, we get
f(x)=x×1x+lnx1=lnx

Therefore,
f(x)>0 for allx(1,)f(x)<0 for allx(0,1)

limx0f(x)=1f(x)>0

for allx(0,1)(1,)

Option D is correct answer.

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