How to find the function period

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A periodic function is a function that repeats its values ​​in a nonzero period.

The period of a function is a number, the addition of which to the function's argument does not change the value of the function.

You will need

• Knowledge of elementary mathematics and the principles of analysis.

Instructions

1

Let's designate the period of the function f (x) in terms of the number K. Our task is to find this value of K. To do this, suppose that the function f (x), using the definition of a periodic function, equals f (x + K) = f (x).

2

We solve the resulting equation for the unknown K, as if x is a constant. Depending on the value of K, there are several options.

3

If K & gt-0 - then this is the period of your function.

If K = 0, then the function f (x) is not periodic.

If the solution of the equation f (x + K) = f (x) does not exist for any K not equal to zero, then such a function is said to be aperiodic, and it also does not have a period.