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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!

Given that f(x) = x + 3 and g(x) = x^2 - x, find (f + g)(4), if it exists.

This problem involves finding the sum of two functions, f(x) = x + 3 and g(x) = x^2 - x, evaluated at x = 4. The step-by-step solution covers the function evaluation process, the addition of functions, and algebraic simplification. Suitable for high school students.

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