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Question

The function f(x)=x+ln(x1+x) is increasing in

A
(1,0)
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B
(,)
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C
only some part of its domain
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D
its domain
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Solution

The correct option is D its domain
Given : f(x)=x+ln(x1+x)
For domain of f(x):x1+x>0
x(,1)(0,)

Now, f(x)=1+1+xx×(1(1+x)2)
=x(1+x)+1x(1+x) =x2+x+1x(1+x)
For increasing, f(x)0
x(1+x)>0 {x2+x+1>0 as a>0,D<0}

x(,1)(0,) which is the domain of the function.

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