0}} \right. \; \left \{ {{x\geq 9} \atop {x<8}} \right. \; \; \Rightarrow \; \; x\in \varnothing" alt="1)\; \; f(x)=\sqrt{x+2}+\frac{x-7}{x^2-4}\\\\OOF:\; \; \left \{ {{x+2\geq 0} \atop {x^2-4\ne 0}} \right. \; \; \left \{ {{x\geq -2} \atop {x\ne -2\; ,\; x\ne 2}} \right. \; \Rightarrow \; \; x\in (-2,2)\cup (2,+\infty )\\\\2)\; \; f(x)=\sqrt{x-9}+\frac{6}{\sqrt{8-x}}\\\\OOF:\; \; \left \{ {{x-9\geq 0} \atop {8-x>0}} \right. \; \left \{ {{x\geq 9} \atop {x<8}} \right. \; \; \Rightarrow \; \; x\in \varnothing" align="absmiddle" class="latex-formula">
0} \atop {x^2-8x+7\ne 0}} \right. \; \left \{ {{x\geq 6\; ,\; x>-3} \atop {x\ne 1\; ,\; x\ne 7}} \right. \; \Rightarrow \; x\in [\, 6,7)\cup (7,+\infty )" alt="3)\; \; f(x)=\frac{\sqrt{x-6}}{\sqrt{x+3}}+\frac{5x-4}{x^2-8x+7}\\\\OOF:\; \; \left \{ {{x-6\geq 0\; ,\; x+3>0} \atop {x^2-8x+7\ne 0}} \right. \; \left \{ {{x\geq 6\; ,\; x>-3} \atop {x\ne 1\; ,\; x\ne 7}} \right. \; \Rightarrow \; x\in [\, 6,7)\cup (7,+\infty )" align="absmiddle" class="latex-formula">