${{D}_{fog}}=\left\{ x\left| x\in {{D}_{g}}\,,\,g(x)\in {{D}_{f}} \right. \right\}=\left\{ x\ne 0\left| g(x)\ge 0 \right. \right\}=\left\{ x\ne 0|\frac{1}{x}\ge 1 \right\}=\left\{ x\ne 0\,,\,0\lt x\le 0 \right\}=(0,\,1]$
${{D}_{f+g}}={{D}_{f}}\bigcap {{D}_{g}}=[1\,,\,+\infty )\bigcap (\mathbb{R}-\left\{ 0 \right\})=[1\,,\,+\infty )$
${{D}_{(\frac{fog}{f+g})}}=(({{D}_{fog}})\bigcap ({{D}_{f+g}}))-\left\{ x\left| (f+g)(x)=0 \right. \right\}=\left\{ 1 \right\}$
بنابراین دامنه این تابع فقط یک عضو دارد.
مهدی خلجی 
