If f ((1-x) / (1 + x)) = (1-x ^ 2) / (1 + x ^ 2), then f (x)=

Let a = (1-x) / (1 + x)
1+a=2/(1+x)
So 1 + x = 2 / (1 + a)
x=(1-a)/(1+a)
(1-x²)/(1+x²)
=[1-(1-a)²/(1+a)²]/[1+(1-a)²/(1+a)²]
Up and down (1 + a) & sup2;
=[(1+a)²-(1-a)²]/[(1+a)²+(1-a)²]
=4a/(2+2a²)
=2a/(1+a²)
That is, f (a) = 2A / (1 + A & sup2;)
So f (x) = 2x / (1 + X & sup2;)

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