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Question

All possible values of x for which the function
f(x)=xlnxx+1 is positive is

A
(1,)
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B
(1e,)
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C
[e,)
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D
(0,){1}
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Solution

The correct option is C (0,){1}
The function is:

f(x)=xlnxx+1

Domain is x>0 for the ln function to exist.

f(x)=x×1x+lnx1

f(x)=lnx

For f'(x) to exist x>0

Intersection of both the domains give for the function to be positive x>0

Only at x=0 we have f(x)=0 hence the The total domain for the function to be positive is (0,)1. ....Answer

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