SOLUTION: If y(x) = x / 1-x , show that 1/2 [y(x) + y(-x)] = y(x^2)

Question 1015396: If y(x) = x / 1-x , show that 1/2 [y(x) + y(-x)] = y(x^2)
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
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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.

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