# Find the period

• December 7th 2009, 04:01 AM
dhiab
Find the period
Find the period of the function :
$
\forall x\in \Re :f(x+1)=\frac{1}{1-f(x)}
$
• December 7th 2009, 10:37 PM
qmech
$f(x+1)=\frac{1}{1-f(x)}
$

$f(x+2)=\frac{1}{1-f(x+1)} = 1 - \frac{1}{f(x)}$

$f(x+3)=\frac{1}{1-f(x+2)} = \frac{1}{1 - {(1-{\frac{1}{f(x)}}})} = f(x)$

so period = 3