Given the functions $f(x) = x^2 + 7$ and $g(x) = 6 - x$, you are asked to find $(f + g)(x)$, which represents the sum of the two functions.

Step-by-step solution:

1. $f(x) = x^2 + 7$

2. $g(x) = 6 - x$

3. To find $(f + g)(x)$, you add the two functions: $(f + g)(x) = f(x) + g(x) = (x^2 + 7) + (6 - x)$

4. Combine like terms: $(f + g)(x) = x^2 - x + 7 + 6 = x^2 - x + 13$

Final Answer:

$(f + g)(x) = x^2 - x + 13$

Would you like further details on this, or do you have any questions?

Here are 5 related questions for further practice:

1. What is $(f - g)(x)$ for the same functions?
2. Find $(f \cdot g)(x)$ for these functions.
3. What is the value of $(f + g)(2)$?
4. Determine the domain of $f(x)$ and $g(x)$.
5. If $f(x) = g(x)$, what is the solution for $x$?

Tip: When adding or subtracting functions, always combine like terms carefully to simplify the result.