نکته: ${{D}_{fog}}=\left\{ x\in {{D}_{g}}\left| g(x)\in {{D}_{f}} \right. \right\}$ ابتدا توجه کنید که ${{D}_{f}}=\left( -\infty ,4 \right]$ و ${{D}_{g}}=\mathbb{R}$. اکنون می‌توان نوشت: ${{D}_{fog}}=\left\{ x\in {{D}_{g}}\left| g(x)\in {{D}_{f}} \right. \right\}=\left\{ x\in \mathbb{R}\left| \sqrt[3]{x-1} \right.\le 4 \right\}$ $=\left\{ x\in \mathbb{R}\left| x-1\le 64 \right. \right\}=\left\{ x\in \mathbb{R}\left| x\le 65 \right. \right\}=\left( -\infty ,65 \right]$