Show that if $f(x)$ is a periodic function with period $P$, then $g(x)=f(kx)$ is also periodic and define a period of the periodic function $g(x)$. Afterwards, find a periodic function with the period of $1$.
I need this for my uni and I'm kinda stuck.
If $f(x)$ has period $P$, then $f(x) = f(x+P)$ for all $x$. Then look at the function $g$. What is the value of $g(x + \frac{P}{k})$? How can you write this in terms of $f$?