Let's solve the problem shown in your image step by step.

You are given two functions:

• $f(x) = x + 3$
• $g(x) = x^2 - x$

The problem asks to find $(f + g)(4)$, which is the sum of the values of the functions $f(4)$ and $g(4)$.

Step 1: Evaluate $f(4)$

The function $f(x)$ is defined as: $f(x) = x + 3$ Substitute $x = 4$ into this expression: $f(4) = 4 + 3 = 7$

Step 2: Evaluate $g(4)$

The function $g(x)$ is defined as: $g(x) = x^2 - x$ Substitute $x = 4$ into this expression: $g(4) = 4^2 - 4 = 16 - 4 = 12$

Step 3: Add $f(4)$ and $g(4)$

Now add the results from Step 1 and Step 2: $(f + g)(4) = f(4) + g(4) = 7 + 12 = 19$

So, $(f + g)(4) = 19$.

Final Answer:

The correct choice is A. $(f + g)(4) = 19$.

Would you like further details or have any questions?

Here are 5 related questions you might consider:

1. What is the general process for adding functions?
2. How would you evaluate $f(x) + g(x)$ for a different value of $x$?
3. What happens if one of the functions is undefined at a certain point?
4. How can you graph the sum of two functions?
5. What if the functions $f(x)$ and $g(x)$ had different domains?

Tip: Always make sure to check the domain of each function before performing operations like addition or subtraction!