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.