I have got the question below for an assignment, I understand how and what the piecewise equation does, but I am wondering if someone can explain what the $f(x)=f(x+2)$ is referring to? Does this mean function of a function?If so, how would I solve this? Question
It means if you know $f(0)$, we know $f(2)$, and we also know $f(4)$. The values are equal.
Similarly for $f(-2)$ and $f(-4)$.
In general, if we know $f(x)$, then we know the values of $f(x+2)$ and $f(x-2)$ and they are equal.
This is a periodic function with period $2$.
The function is first defined on $[-1,1]$ and then extended to the whole line by adding the condition $f(x+2)=f(x)$ (periodocity of $f$). For example, if $7 \leq x \leq 9$ then $x-8$ lies between $-1$ and $1$ and $f(x)$ is defined to be $f(x-8x)$. [Note that $f(x+2)=f(x)$ for all $x$ implies that $f(x+2n)=f(x)$ for all $x$ and for any integer $n$].