The problem shown in your image involves finding the sum of two functions $f(x) = 7x - 9$ and $g(x) = 5 - x$, and then simplifying their sum.

Step-by-Step Solution:

We are given the two functions:

• $f(x) = 7x - 9$
• $g(x) = 5 - x$

The sum of the functions is: $(f + g)(x) = f(x) + g(x)$ Substitute the given functions: $(f + g)(x) = (7x - 9) + (5 - x)$ Now, combine like terms: $(f + g)(x) = 7x - x - 9 + 5$ $(f + g)(x) = 6x - 4$

Thus, the sum of the functions is: $(f + g)(x) = 6x - 4$

Would you like details on further parts of the problem or clarification? Here are some questions to extend your understanding:

1. How would you find $(f - g)(x)$?
2. Can you determine $(f \cdot g)(x)$ by multiplying $f(x)$ and $g(x)$?
3. What happens if you need to divide $f(x)$ by $g(x)$?
4. How would you find the domain of $\frac{f(x)}{g(x)}$?
5. How can the sum $f(x) + g(x)$ change if either function changes form?

Tip: When combining functions, always be careful with the signs and distribution, especially when subtracting functions!