\( (\mathrm{f}-\mathrm{g})(\mathrm{x})=\sqrt{\mathrm{x}-9}-\sqrt{9-\mathrm{x}} \mathrm{s} \) What is the domain of \( \mathrm{f}-\mathrm{g} \) ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain of \( \mathrm{f}-\mathrm{g} \) is \( \{ \). (Use a comma to separate answers as needed.) B. The domain of \( \mathrm{f}-\mathrm{g} \) is (Type your answer in interval notation.) C . The domain of \( \mathrm{f}-\mathrm{g} \) is \( \varnothing \).

To find the domain of \( (\mathrm{f}-\mathrm{g})(\mathrm{x})=\sqrt{\mathrm{x}-9}-\sqrt{9-\mathrm{x}} \), we must determine where both components, \( \sqrt{\mathrm{x}-9} \) and \( \sqrt{9-\mathrm{x}} \), are defined. The first term, \( \sqrt{\mathrm{x}-9} \), requires that \( \mathrm{x} \geq 9 \). The second term, \( \sqrt{9-\mathrm{x}} \), requires that \( \mathrm{x} \leq 9 \). Combining these inequalities, we find that the only value of \( \mathrm{x} \) that satisfies both conditions simultaneously is \( \mathrm{x} = 9 \). Therefore, the domain of \( \mathrm{f}-\mathrm{g} \) is simply \( \{ 9 \} \). So, the final answer is: A. The domain of \( \mathrm{f}-\mathrm{g} \) is \( \{ 9 \} \).