Find the period of the function : $\displaystyle \forall x\in \Re :f(x+1)=\frac{1}{1-f(x)} $
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$\displaystyle f(x+1)=\frac{1}{1-f(x)} $ $\displaystyle f(x+2)=\frac{1}{1-f(x+1)} = 1 - \frac{1}{f(x)}$ $\displaystyle f(x+3)=\frac{1}{1-f(x+2)} = \frac{1}{1 - {(1-{\frac{1}{f(x)}}})} = f(x)$ so period = 3
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