Is the quotient of periodic functions also periodic?

AI Thread Summary
The discussion centers on proving that if a function f is periodic with period P, then 1/f is also periodic with the same period P. Participants express uncertainty about how to demonstrate this, particularly whether 1/f(s + P) equals 1/f(s). There is also a related question regarding the periodicity of the quotient of two periodic functions, f and g, suggesting that the resulting period could be smaller than P. An example is requested to illustrate this concept. The conversation highlights the challenges in proving periodicity for function quotients.
Kyyzen
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Homework Statement


Let f be periodic with period P. Prove that 1/f is periodic with period P.


The Attempt at a Solution



f(s+P)= f(s) I know that is the equation for a periodic function. I am not sure how to
prove the 1/f part though. Would I just do this:

1/f(s+P)=f(s)? I'm just not sure what exactly to do. Please help =D haha.

*ALSO* I have another question that states.
Let f, g be periodic with period P. Prove that f/g is periodic, but the period could be smaller than P. In addition, give an example that illustrates this.

I have not attempted this one yet.
 
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Kyyzen said:

Homework Statement


Let f be periodic with period P. Prove that 1/f is periodic with period P.


The Attempt at a Solution



f(s+P)= f(s) I know that is the equation for a periodic function. I am not sure how to
prove the 1/f part though. Would I just do this:

1/f(s+P)=f(s)?
No. Don't you need to show that 1/f(s + P) = 1/f(s)?
Kyyzen said:
I'm just not sure what exactly to do. Please help =D haha.

*ALSO* I have another question that states.
Let f, g be periodic with period P. Prove that f/g is periodic, but the period could be smaller than P. In addition, give an example that illustrates this.

I have not attempted this one yet.
 

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