https://file.aiquickdraw.com/mathbot/file/172744263218507cxz0hc.jpg

To solve \( (f \circ g)(5) \), we need to find \( g(5) \) first and then use that value to find \( f(g(5)) \).

### Step 1: Find \( g(5) \)
From the graph:
- The black line represents the function \( g(x) \).
- Looking at the graph, the point where \( x = 5 \) on the black line corresponds to \( g(5) = -6 \).

### Step 2: Find \( f(g(5)) = f(-6) \)
- The blue line represents the function \( f(x) \).
- Looking at the blue line, the point where \( x = -6 \) corresponds to \( f(-6) = 36 \).

Thus, \( (f \circ g)(5) = f(g(5)) = f(-6) = 36 \).

The final answer is:

\[
(f \circ g)(5) = 36
\]

Would you like more details or have any questions? Here are five related questions to deepen your understanding:

1. What is the general process for solving composite functions?
2. How do you find the inverse of a composite function \( (f \circ g)^{-1}(x) \)?
3. How does the slope of a linear function affect its behavior on a graph?
4. What are the domain and range of \( f(x) \) and \( g(x) \) in this example?
5. How do you interpret the intersection point of two functions on a graph?

**Tip:** When working with composite functions, always evaluate the innermost function first before applying the outer function.

The blue and black curves on the graph below represent f(x) and g(x), respectively. Find (f ∘ g)(5).

Learn how to solve the composite function (f ∘ g)(5) using a graph. The problem involves interpreting linear functions from the graph to find g(5) and f(g(5)), suitable for high school students in grades 9-11.

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