Questions: Find (f+g, f-g, fg) and (fracfg). Determine the domain for each function. [f(x)=3x+2, g(x)=x-9] ((f+g)(x)=4x-7) (Simplify your answer.) What is the domain of (f+g)? A. The domain of (f+g) is (square) - (Type your answer in interval notation.) B. The domain of (f+g) is (square) . (Use a comma to separate answers as needed.) C. The domain of (f+g) is (varnothing).

Find (f+g, f-g, fg) and (fracfg). Determine the domain for each function. [f(x)=3x+2, g(x)=x-9] ((f+g)(x)=4x-7) (Simplify your answer.) What is the domain of (f+g)? A. The domain of (f+g) is (square) - (Type your answer in interval notation.) B. The domain of (f+g) is (square) . (Use a comma to separate answers as needed.) C. The domain of (f+g) is (varnothing).
Transcript text: Find $f+g, f-g, f g$ and $\frac{f}{g}$. Determine the domain for each function. \[ f(x)=3 x+2, g(x)=x-9 \] $(f+g)(x)=4 x-7$ (Simplify your answer.) What is the domain of $f+g$ ? A. The domain of $f+g$ is $\square$ - (Type your answer in interval notation.) B. The domain of $f+g$ is $\square$ \}. (Use a comma to separate answers as needed.) C. The domain of $f+g$ is $\varnothing$.
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Solution

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Solution Steps

Step 1: Addition of $f(x)$ and $g(x)$

The sum of $f(x)$ and $g(x)$ is: $4 x - 7$. The domain is $(-\infty, \infty)$.

Step 2: Subtraction of $f(x)$ and $g(x)$

The difference of $f(x)$ and $g(x)$ is: $2 x + 11$. The domain is $(-\infty, \infty)$.

Step 3: Multiplication of $f(x)$ and $g(x)$

The product of $f(x)$ and $g(x)$ is: $\left(x - 9\right) \left(3 x + 2\right)$. The domain is $(-\infty, \infty)$.

Step 4: Division of $f(x)$ by $g(x)$

The quotient of $f(x)$ by $g(x)$ is: $\frac{3 x + 2}{x - 9}$. The domain is $(-\infty, \infty)$ excluding $9$.

Final Answer:

Addition: $4 x - 7$, Subtraction: $2 x + 11$, Multiplication: $\left(x - 9\right) \left(3 x + 2\right)$, Division: $\frac{3 x + 2}{x - 9}$ with domain considerations as mentioned.

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