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If f(x) is a periodic function with period p, show that the function f(a x) (where a is a non-zero constant) is periodic with period p / a .

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Final answer:

If f(x) is a periodic function with period p, then the function f(a x), where a is a non-zero constant, is periodic with period p/a.

Step-by-step explanation:

A periodic function is a function that repeats itself after a certain interval called the period. If we have a periodic function f(x) with period p, and we multiply the argument of the function by a constant 'a', we get the function f(a x), where 'a' is a non-zero constant.

To show that f(a x) is periodic with period p/a, we can substitute 'a x' in place of 'x' in the original periodic function f(x). This gives us f(a x) which repeats itself every p/a units of 'a x', hence it is periodic with period p/a.

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