0} \atop {x-2\geqslant 0}} \right.\quad\rightarrow\quad\left \{ {{x<5} \atop {x\geqslant2}} \right. \quad\rightarrow\quad\boxed{x\in[2;5)}" alt="\displaystyle f(x)=\lg(5-x)+\sqrt{x-2}\\\\\left \{ {{5-x>0} \atop {x-2\geqslant 0}} \right.\quad\rightarrow\quad\left \{ {{x<5} \atop {x\geqslant2}} \right. \quad\rightarrow\quad\boxed{x\in[2;5)}" align="absmiddle" class="latex-formula">