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If y(x) = x / 1-x , show that 1/2 [y(x) + y(-x)] = y(x^2)
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y(x) = ,
y(-x) = = .
Therefore,
y(x) + y(-x) = - = (now write it with the common denominator, which is (1-x)*(1+x) )
= - =
= = .
Therefore,
. = .
It is what has to be proved.