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Question

the function f:RR defined as
f(x)=12ln(x2+1+xx2+1x)2is

A
One -one and onto both
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B
One-one but not onto
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C
Onto but not one-one
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D
Niether one-one nor onto
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Solution

The correct option is A Niether one-one nor onto
Given,
f(x)=12ln(x2+1+x+x2+1x

Now putting
x(x)

We get,
f(x)=12ln((x)2+1+x+(x)2+1fx)
f(x)=12ln(x2+1x+x2+1+x

f(x)=f(x)

Therefore f(x) is an even function.
and even functions are many on 0 .

Now we know,
x2+1>0;xR
and
x2+1+x+x2+1x>1

f(x)>0

- Given, f:RR.
and co domain R.

Option D function is neither onto nor one one.


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