$$ 1 \leftarrow $$ For the functions $$ f(x)=6-x^{2} $$ and $$ g(x)=x^{2}+4 x-32 $$, find $$ f+g, f-g $$, $$ f $$, and $$ \frac{f}{g} $$. Determine the domain for each function. $$ (f+g)(x)=4 x-26 $$ (Simplify your answer.). What is the domain of $$ f+g $$ ? Select the correct choice below and, if necessary, fill in the answer box to complete $$ y $$ choice. A. The domain of $$ f+g $$ is $$ \} $$. (Use a comma to separate answers as needed.) B. The domain of $$ f+g $$ is (Type your answer in interval notation.) C. The domain of $$ f+g $$ is $$ \varnothing $$.

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To determine the domain of the function $$ f + g $$, let's analyze the functions $$ f(x) $$ and $$ g(x) $$:

- **Function Definitions:**
  $$
  f(x) = 6 - x^2
  $$
  $$
  g(x) = x^2 + 4x - 32
  $$

- **Sum of the Functions:**
  $$
  (f + g)(x) = f(x) + g(x) = (6 - x^2) + (x^2 + 4x - 32) = 4x - 26
  $$

- **Determining the Domain:**
  
  Both $$ f(x) $$ and $$ g(x) $$ are polynomials. Polynomial functions are defined for all real numbers. Therefore, the domain of $$ f + g $$ is the intersection of the domains of $$ f(x) $$ and $$ g(x) $$.

$$
  \text{Domain of } f(x): \mathbb{R}
  $$
  $$
  \text{Domain of } g(x): \mathbb{R}
  $$
  $$
  \text{Domain of } f + g: \mathbb{R} \cap \mathbb{R} = \mathbb{R}
  $$

In interval notation, this is represented as $$ (-\infty, \infty) $$.

- **Answer Choice:**

**B.** The domain of $$ f + g $$ is $$ (-\infty, \infty) $$.
The domain of $$ f + g $$ is all real numbers, which can be written as $$ (-\infty, \infty) $$.

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