https://file.aiquickdraw.com/mathbot/file/1726977157207hb3wm0r5.jpg

The problem in your image provides two functions:

- \( f(x) = x - 3 \)
- \( g(x) = x^2 - x \)

You are asked to find and simplify the expression \( (f + g)(6) \).

### Step-by-Step Solution:
1. The expression \( (f + g)(6) \) means we need to evaluate the sum of the two functions \( f(x) \) and \( g(x) \) at \( x = 6 \).
   
2. First, calculate \( f(6) \):
   \[
   f(6) = 6 - 3 = 3
   \]

3. Next, calculate \( g(6) \):
   \[
   g(6) = 6^2 - 6 = 36 - 6 = 30
   \]

4. Now, sum the values of \( f(6) \) and \( g(6) \):
   \[
   (f + g)(6) = f(6) + g(6) = 3 + 30 = 33
   \]

So, the simplified expression is:
\[
(f + g)(6) = 33
\]

Would you like any further details or clarifications?

Here are five related questions for further practice:
1. What is \( (f + g)(x) \) in general form?
2. What is \( (f - g)(6) \)?
3. How do you evaluate \( (f \times g)(6) \)?
4. What is the derivative of \( f(x) \) and \( g(x) \)?
5. Can you compute \( f(g(6)) \) and \( g(f(6)) \)?

**Tip**: Always apply the functions step by step, especially when dealing with compositions or sums, to avoid calculation mistakes!

Let f(x) = x - 3 and g(x) = x^2 - x. Find and simplify the expression (f + g)(6).

Learn how to simplify the expression (f + g)(6) where f(x) = x - 3 and g(x) = x^2 - x. This problem involves adding functions and evaluating them at x = 6. Suitable for students in Grades 9-11.

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