For the functions $$ f(x)=7-x^{2} $$ and $$ g(x)=x^{2}+4 x-45 $$, fii $$ (f+g)(x)=2 x^{2}+4 x-38 $$ (Simplify your answer.)

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Simplify the expression by following steps:
- step0: Simplify:
  $$\left(7-x^{2}\right)+\left(x^{2}+4x-45\right)$$
- step1: Remove the parentheses:
  $$7-x^{2}+x^{2}+4x-45$$
- step2: Subtract the numbers:
  $$-38+4x$$
To find $$ (f+g)(x) $$, we need to add the two functions $$ f(x) $$ and $$ g(x) $$:

1. **Identify the functions:**
   - $$ f(x) = 7 - x^2 $$
   - $$ g(x) = x^2 + 4x - 45 $$

2. **Add the functions:**
   $$
   (f+g)(x) = f(x) + g(x) = (7 - x^2) + (x^2 + 4x - 45)
   $$

3. **Combine like terms:**
   - The $$ -x^2 $$ and $$ +x^2 $$ cancel each other out.
   - Combine the constant terms: $$ 7 - 45 = -38 $$.
   - The linear term is $$ 4x $$.

Thus, we have:
$$
(f+g)(x) = -38 + 4x
$$

4. **Final simplified form:**
$$
(f+g)(x) = 4x - 38
$$

So, the simplified answer is $$ (f+g)(x) = 4x - 38 $$.
$$ (f+g)(x) = 4x - 38 $$

For the functions \( f(x)=7-x^{2} \) and \( g(x)=x^{2}+4 x-45 \), fii \( (f+g)(x)=2 x^{2}+4 x-38 \) (Simplify your answer.)

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