Hàm số xác định khi và chỉ khi \(\left\{\begin{array}{l}2024-1012 x \geq 0 \\ |2 x-1|-x \neq 0\end{array} \quad\left(^{*}\right)\right.\).

Xét \(|2 x-1|-x=0 \Leftrightarrow|2 x-1|=x \Leftrightarrow\) \(\left\{\begin{array}{l}x \geq 0 \\ {\left[\begin{array}{l}2 x-1=x \\ 2 x-1=-x\end{array}\right.}\end{array}\right.\)\(\Leftrightarrow\left\{\begin{array}{l}x \geq 0 \\ {\left[\begin{array}{l}x=1 \\ x=\frac{1}{3}\end{array}\right.}\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{l}x=1 \\ x=\frac{1}{3}\end{array}\right.\)

Do vậy \((*) \Leftrightarrow\left\{\begin{array}{l}x \leq 2 \\ x \neq 1, x \neq \frac{1}{3}\end{array}\right.\). Tập xác định hàm số: \(D=(-\infty ; 2] \backslash\left\{1 ; \frac{1}{3}\right\}\).