4. Let \( f(x) = \begin{cases} 
x - [x], & x \leqslant 0 \\ 
f(x-1), & x > 0 
\end{cases} \), where \([x]\) denotes the greatest integer less than or equal to \(x\). If \( f(x) = kx + k \) (where \( k > 0 \)) has three distinct real roots, then the range of the real number \( k \) is \(\qquad\).
4. $\left(\frac{1}{4}, \frac{1}{3}\right.$



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4. $\left(\frac{1}{4}, \frac{1}{3}\right.$