Question: what is the sum of $f(x)=x+3$, $g(x)=-x+7$
1. **State the problem:** We need to find the sum of the functions $f(x)=x+3$ and $g(x)=-x+7$.
2. **Formula for sum of functions:** The sum of two functions $f(x)$ and $g(x)$ is given by:
$$ (f+g)(x) = f(x) + g(x) $$
3. **Apply the formula:** Substitute the given functions:
$$ (f+g)(x) = (x+3) + (-x+7) $$
4. **Simplify the expression:**
$$ (f+g)(x) = x + 3 - x + 7 $$
5. **Cancel common terms:**
$$ (f+g)(x) = \cancel{x} + 3 - \cancel{x} + 7 $$
6. **Combine like terms:**
$$ (f+g)(x) = 3 + 7 = 10 $$
**Final answer:**
$$ (f+g)(x) = 10 $$
This means the sum of the two functions is a constant function equal to 10 for all $x$.