Is the quotient of periodic functions also periodic?

[Kyyzen]

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.

 

[Mark44]

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)?

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.