# Math Help - Period : 2

1. ## Period : 2

Find the period for the function f in R:
f(x+1)f(x)+f(x+1)+1=f(x)

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

Replace x with x+1:

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

Replace x with x+2:

$f(x+4)=-\frac{1}{f(x+2)}=-\frac{1}{\displaystyle -\frac{1}{f(x)}}=f(x)$.

Then the period is 4.