Find $$ \mathrm{f}+\mathrm{g}, \mathrm{f}-\mathrm{g} $$, fg, and $$ \frac{\mathrm{f}}{\mathrm{g}} $$. Determine the domain for each function. $$ f(x)=\sqrt{x} ; g(x)=x-9 $$ What is the domain of $$ \frac{f}{g} $$ ? A. The domain of $$ \frac{\mathrm{f}}{\mathrm{g}} $$ is $$ \square $$ (Type your answer in interval notation.) B. The domain of $$ \frac{f}{g} $$ is $$ \square $$ (Use a comma to separate answers as needed.)

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To determine the domain of the function $$ \frac{f}{g} = \frac{\sqrt{x}}{x - 9} $$, we need to consider two conditions:

1. **Square Root Constraint:** The expression inside the square root must be non-negative.
   $$
   x \geq 0
   $$
   
2. **Denominator Constraint:** The denominator cannot be zero.
   $$
   x - 9 \neq 0 \implies x \neq 9
   $$

Combining these conditions, the domain of $$ \frac{f}{g} $$ consists of all real numbers $$ x $$ such that $$ x $$ is greater than or equal to 0 **and** $$ x $$ is not equal to 9.

### Answer:

**A.** The domain of $$ \frac{\mathrm{f}}{\mathrm{g}} $$ is $$[0, 9) \cup (9, \infty)$$.

**B.** The domain of $$ \frac{\mathrm{f}}{\mathrm{g}} $$ is $$ [0, 9) , (9, \infty) $$.
The domain of $$ \frac{f}{g} $$ is all real numbers $$ x $$ where $$ x \geq 0 $$ and $$ x \neq 9 $$. In interval notation, this is $$[0, 9) \cup (9, \infty)$$.

Find , fg, and . Determine the domain for each function.

What is the domain of ?
A. The domain of is (Type your answer in interval notation.)
B. The domain of is (Use a comma to separate answers as needed.)

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Find , fg, and . Determine the domain for each function. What is the domain of ? A. The domain of is (Type your answer in interval notation.) B. The domain of is (Use a comma to separate answers as needed.)