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Question

Let f:(12,1](, ln2 ] be a function defined as f(x)=ln(x+1x2) and g(x)=x2f(x) .
If f(x0)=ln2, then

A
g(x0)=12 ln2
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B
g(x0)=log2e
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C
g(x0)=22 log2e
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D
g(x0)=2 loge2
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Solution

The correct option is C g(x0)=22 log2e
f(x0)=ln2=ln(x0+1x20)
(2x0)2=1x20
2+x2022x0=1x20
2x2022x0+1=0
x0=22 ± 02×2x0=12
So g(x0)=12×1ln2=log2e
g(x)=f(x).2xx2f(x)f2(x)g(x0)=22log2 e
Because, f(x0)=0.

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