4. Let $f(x)=\left\{\begin{array}{ll}x-[x], & x \leqslant 0 ; \\ f(x-1), & x>0,\end{array}\right.$ where $[x]$ denotes the greatest integer not exceeding the real number $x$. If $f(x)=k x+k(k>0)$

has: different real roots, then the range of the real number $k$ is . $\qquad$
4. $k \in\left[\frac{1}{4}, \frac{1}{3}\right)$.