F(x)+g(x) is also periodic

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In summary, a periodic function repeats its values at regular intervals, while a non-periodic function does not. Two periodic functions with the same period can be added together to create another periodic function with the same period. The period of the sum of two periodic functions is the least common multiple of the individual periods. To determine if the sum of two periodic functions is also periodic, you can compare the periods of the individual functions and see if they are equal or have a common multiple.
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Cemre
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Hello,

correct me if I am wrong, but as far as I know if 2 functions f(x) and g(x) are periodic with Tf and Tg periods. f(x)+g(x) is also periodic with least common multiple of Tf and Tg.

But; what if that least common multiple doesn't exist?

is "sin(x) + sin(pi*x)" periodic?

there is no x ( except for zero ) which makes both sin(x) and sin(pi*x) zero at the same x.

Regards.
 
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The quotient of the periods, Tf/Tg has to be rational in order for the sum to be periodic.
 

1. What does it mean for a function to be periodic?

A periodic function is a function that repeats its values at regular intervals. This means that the output of the function will have the same values at specific intervals of the input variable.

2. How is a periodic function different from a non-periodic function?

A non-periodic function does not repeat its values at regular intervals. This means that the output of the function will have different values for different inputs, unlike a periodic function which has the same values at specific intervals.

3. Can two periodic functions be added together to create another periodic function?

Yes, if two periodic functions have the same period (interval of repetition), then their sum will also be a periodic function with the same period. This is because the values of both functions will repeat at the same intervals, resulting in a periodic pattern.

4. What is the period of the sum of two periodic functions?

The period of the sum of two periodic functions is the least common multiple of the individual periods of the two functions. This is because the sum function will repeat its values at intervals that are common to both individual functions.

5. How can I determine if the sum of two periodic functions is also periodic?

To determine if the sum of two periodic functions is also periodic, you can compare the periods of the individual functions. If the periods are equal, then the sum will also be periodic. If the periods are not equal, then the sum may still be periodic if their periods have a common multiple.

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