# Thread: Periodicity of a function

1. ## Periodicity of a function

Hello. I need some help on solving the following problem

Review the periodicity of the following function:

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

Thanks in advance.

2. Originally Posted by javax
Hello. I need some help on solving the following problem

Review the periodicity of the following function:

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

Thanks in advance.
This function is clearly not periodic.

3. In general rational functions, including polynomials, are NOT periodic.

4. Just to clarify, the function you have given is a rational function, ie. it can be written as the quotient of two polynomials. Almost all rational functions are not periodic. The exceptions are the constant functions which are very periodic (they have period p for every p).