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To solve the composite function \( f(g(6)) \) using the graphs provided:

1. **Find \( g(6) \)**: 
   - Look at the graph of \( g(x) \) (the red line) and locate where \( x = 6 \).
   - From the graph, it appears that \( g(6) = -4 \), as the red graph intersects the point \( (6, -4) \).

2. **Find \( f(g(6)) = f(-4) \)**:
   - Now, using \( g(6) = -4 \), we need to find \( f(-4) \).
   - Look at the graph of \( f(x) \) (the blue line) and locate where \( x = -4 \).
   - From the graph, it seems that \( f(-4) = 6 \), as the blue graph intersects the point \( (-4, 6) \).

Thus, \( f(g(6)) = f(-4) = 6 \).

Would you like a more detailed explanation of any step?

Here are 5 related questions to deepen your understanding:
1. What is the significance of composite functions in real-life applications?
2. How would you evaluate \( g(f(x)) \) using the same graphs?
3. What happens if you input a value that is not on the graph?
4. Can composite functions be represented algebraically? How?
5. What properties of functions are important to understand when working with their graphs?

**Tip**: Always verify that you're reading the correct function by noting color, line style, or labels to avoid confusion!

Use the graphs of f and g to evaluate the composite function f(g(6)).

Learn how to evaluate the composite function f(g(6)) using the provided graphs of f and g. This problem involves understanding composite functions and interpreting graphs. Suitable for students in Grades 9-12.

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