Questions: Find (f+g), (f-g), (f g) and (fracfg). Determine the domain for each function. (f(x)=4 x+7), (g(x)=x+1) ((f-g)(x)=3 x+6) (Simplify your answer.) What is the domain of (f-g) ? A. The domain of (f-g) is ((-∞, ∞)). (Type your answer in interval notation.) B. The domain of (f-g) is (). (Use a comma to separate answers as needed.) C. The domain of (f-g) is (varnothing). ((f g)(x)=) (Simplify your answer.)

Find (f+g), (f-g), (f g) and (fracfg). Determine the domain for each function.
(f(x)=4 x+7), (g(x)=x+1)
((f-g)(x)=3 x+6) (Simplify your answer.)
What is the domain of (f-g) ?
A. The domain of (f-g) is ((-∞, ∞)). (Type your answer in interval notation.)
B. The domain of (f-g) is (). (Use a comma to separate answers as needed.)
C. The domain of (f-g) is (varnothing).
((f g)(x)=)
(Simplify your answer.)
Transcript text: Find $f+g, f-g, f g$ and $\frac{f}{g}$. Determine the domain for each function. \[ f(x)=4 x+7, g(x)=x+1 \] $(f-g)(x)=3 x+6$ (Simplify your answer.) What is the domain of $f-g$ ? A. The domain of $f-g$ is $(-\infty, \infty)$. (Type your answer in interval notation.) B. The domain of $f-g$ is $\}$. (Use a comma to separate answers as needed.) C. The domain of $\mathrm{f}-\mathrm{g}$ is $\varnothing$. \[ (f g)(x)=\square \] (Simplify your answer.)
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Solution

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Solution Steps

Step 1: Define the Functions

Given: \[ f(x) = 4x + 7 \] \[ g(x) = x + 1 \]

Step 2: Find \( f + g \)

\[ (f + g)(x) = f(x) + g(x) \] \[ (f + g)(x) = (4x + 7) + (x + 1) \] \[ (f + g)(x) = 4x + x + 7 + 1 \] \[ (f + g)(x) = 5x + 8 \]

Step 3: Find \( f - g \)

\[ (f - g)(x) = f(x) - g(x) \] \[ (f - g)(x) = (4x + 7) - (x + 1) \] \[ (f - g)(x) = 4x - x + 7 - 1 \] \[ (f - g)(x) = 3x + 6 \]

Final Answer

  1. \( (f + g)(x) = 5x + 8 \)
  2. \( (f - g)(x) = 3x + 6 \)
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