Hello, Monster32432421!
You solved it? . . . Good for you!
It's a strange problem . . .
The function $\displaystyle f(x)$ is defined by: .$\displaystyle f(x) \:=\: x^3x\;\text{ for }\text{}1 \leq x < 0$
and $\displaystyle f(x+1) \:=\: f(x)\;\text{ for all real }x.$
Find an expression for $\displaystyle f(x)\:\text{ for }0 \leq x < 1$
$\displaystyle f(x) \:=\:x^3x$ has this graph:
Code:

* 
* *  *
* *

  *     *     *  
1  1
* *
*  * *
 *

For the domain $\displaystyle [\text{}1,0)$, we have this graph:
Code:

* 
* * 
* *

  *     *    
1 0

Since $\displaystyle f(x+1) = f(x), $ the graph on $\displaystyle [0,1)$ is identical to the graph on $\displaystyle [\text{}1,0)$
The graph looks like this:
Code:

*  *
* *  * *
* ** *

  *     *     *  
1 0 1

So the graph of: $\displaystyle f_1(x) \:=\:x^3x$ . is moved one unit to the right.
We have: .$\displaystyle f_2(x) \;=\;(x1)^3  (x1) \:=\:x^3  3x^2 + 2x$
Therefore: .$\displaystyle f(x) \;=\;\begin{Bmatrix}x^3x && \text{}1 \leq x < 1 \\
x^33x^2+2x && 0 \leq x < 1 \end{Bmatrix}$