log f(x) = log[1+(∆f(x) /f(x)) ]
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Step-by-step explanation:
Since, f(x)=log(
1−x
1+x
)
∴f(
1+xy
x+y
)=log(
1−
1+xy
x+y
1+
1+xy
x+y
)
=log(
1+xy−x−y
1+xy+x+y
)
Now, f(x)+f(y)=log(
1−x
1+x
)+log(
1−y
1+y
)
=log(
(1−x)(1−y)
(1+x)(1+y)
)
=log(
1+xy−x−y
1+x+y+xy
)
∴f(
1+xy
x+y
)=f(x)+f(y)
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