function pieriod deduction

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Hi guys!
I don't have an idea how to solve this exercise about function period. Can you explain it to me?
Thanks in advance!
 

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f(x+2)= f((x+1)+ 1)= (1+ f(x+1))(1- f(x+1))= (1+ (1+ f(x))/(1- f(x)))/(1- (1+ f(x))/(1- f(x))).
Now do the tedious algebra!
 
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