# Periodicity of a function

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• January 9th 2011, 01:13 PM
javax
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.
• January 9th 2011, 01:17 PM
mr fantastic
Quote:

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.
• January 9th 2011, 03:33 PM
HallsofIvy
In general rational functions, including polynomials, are NOT periodic.
• January 9th 2011, 05:29 PM
DrSteve
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).