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a1b2c3zzz
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Homework Statement
Prove that if f and g are periodic with period p , then f/g is also periodic, but its period could be smaller than p.
The Attempt at a Solution
So, the first part seems simple enough.
##\frac{f(x+p)}{g(x+p)}=\frac{f}{g}(x + p)=\frac{f}{g}(x)##
But how exactly do I show that the period could be smaller? Here's what I'm thinking:
##\frac{-f}{-g}(x)=\frac{f}{g}(x)##
and what I get from this is that the values of the function would repeat at another interval (where they are both negative) as well as the interval np. However, I could be looking at this entirely the wrong way. Any hints you guys can give me?