Given the functions:

$f(x) = 4x + 4$

$g(x) = 3x + 5$

To find $(f + g)(x)$, you need to add $f(x)$ and $g(x)$:

$(f + g)(x) = f(x) + g(x)$

Substituting the expressions for $f(x)$ and $g(x)$:

$(f + g)(x) = (4x + 4) + (3x + 5)$

Simplify by combining like terms:

$(f + g)(x) = 4x + 3x + 4 + 5 = 7x + 9$

So, $(f + g)(x) = 7x + 9$.

Would you like more details, or do you have any other questions?

Here are 5 related questions to expand on this topic:

1. How would you find $(f - g)(x)$ given $f(x)$ and $g(x)$?
2. How do you calculate $(f \cdot g)(x)$ for the given functions?
3. What is $\frac{f}{g}(x)$ for the given functions?
4. How can you determine the roots of the function $(f + g)(x)$?
5. How do transformations affect the graph of $(f + g)(x)$?

Tip: Always combine like terms carefully when adding or subtracting functions to avoid errors in simplification.