Is it a periodic function?

Level 2

$y$ is a function that satisfies the following $y(x+1) = \dfrac{1-y(x)}{1+y(x)}$

If you think that $y$ is a periodic function, find its fundamental period?

5 4

y

is not a periodic function 3 2

1 solution

Ossama Ismail
May 12, 2020

A function $y$ is said to be periodic if, for some nonzero constant $p$ , it is the case that $\ \ y(x+p)=y(x)$

$y(x+2) = \dfrac { 1- \dfrac{1-y(x)}{1+y(x)}} {1+ \dfrac {1-y(x)}{1+y(x)}} = y(x)$

From the above equation, we can see that $y$ is a periodic function that repeats its values at regular intervals/periods $=2$ .