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The problem asks to evaluate \( f(g(-5)) \) using the graphs of two functions: \( y = f(x) \) and \( y = g(x) \).

### Step-by-Step Solution:

1. **Find \( g(-5) \):**
   - To find \( g(-5) \), locate \( x = -5 \) on the graph of \( g(x) \). 
   - From the graph, at \( x = -5 \), \( g(x) \) appears to be \( 2 \). 
   - Thus, \( g(-5) = 2 \).

2. **Find \( f(g(-5)) = f(2) \):**
   - Now, use the value \( g(-5) = 2 \) and substitute it into \( f(x) \) to find \( f(2) \).
   - Locate \( x = 2 \) on the graph of \( f(x) \).
   - From the graph, at \( x = 2 \), \( f(x) = -1 \).
   - Thus, \( f(2) = -1 \).

3. **Conclusion:**
   - The value of \( f(g(-5)) \) is \( f(2) = -1 \).

### Final Answer:
\[ f(g(-5)) = -1 \]

Would you like further details or have any questions?

Here are some related questions you might explore:
1. What is the composition of functions, and how is it applied?
2. How do you determine the domain and range of composite functions?
3. How can you find the inverse of a function graphically?
4. What does it mean for two functions to be inverses of each other?
5. How do transformations affect the graph of a function?

**Tip:** When evaluating composite functions, always start from the inside out—first find the inner function value, then use that result in the outer function.

Evaluate f(g(-5)) using the graphs of y = f(x) and y = g(x).

Learn how to evaluate composite functions using graphs. This example demonstrates how to find f(g(-5)) using the graphs of f(x) and g(x). Suitable for students in Grades 9-11. Covers concepts of function composition and graph interpretation.

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