$Ifdomainof\left|x\right|+x-\left[x\right]is(0,3),thenitsrangeis$

$\begin{array}{l}f\left(x\right)=\left|x\right|+x-\left[x\right]\\ ifx\in (0,3)then\left|x\right|=x\\ \left[x\right]=\{\begin{array}{l}0if0<x<1\\ 1if1\le x<2\\ 2if2\le x<3\end{array}\\ \therefore f\left(x\right)=\{\begin{array}{l}2xif0<x<1\\ 2x-1if1\le x<2\\ 2x-2if2\le x<3\end{array}\\ if0<x<1,if1\le x<2,if2\le x<3\\ \Rightarrow 0<2x<1,\Rightarrow 2\le 2x<4,\Rightarrow 4\le 2x<6\\ \Rightarrow 1\le 2x-1<3,\Rightarrow 2\le 2x-2<4\\ \therefore Range=(0,4)\end{array}$