Let's analyze the problem using the given graphs. The goal is to evaluate the expressions based on the two functions provided in the graphs: $f(x)$ and $g(x)$.

Here are the step-by-step evaluations:

1. $f(g(2))$:

   • First, find $g(2)$ using the graph on the right.
   • Locate $x = 2$ on the $g(x)$ graph. The corresponding $y$-value (or $g(2)$) is 3.
   • Now, use this result to find $f(3)$ on the left graph (where $x = 3$).
   • The $y$-value at $x = 3$ on the $f(x)$ graph is 1.
   • Therefore, $f(g(2)) = f(3) = 1$.

2. $g(f(4))$:

   • First, find $f(4)$ using the graph on the left.
   • Locate $x = 4$ on the $f(x)$ graph. The corresponding $y$-value (or $f(4)$) is 0.
   • Now, use this result to find $g(0)$ on the right graph (where $x = 0$).
   • The $y$-value at $x = 0$ on the $g(x)$ graph is 2.
   • Therefore, $g(f(4)) = g(0) = 2$.

3. $f(1)$:

   • Locate $x = 1$ on the $f(x)$ graph.
   • The $y$-value at $x = 1$ is 2.
   • Therefore, $f(1) = 2$.

4. $g(5)$:

   • Locate $x = 5$ on the $g(x)$ graph.
   • The $y$-value at $x = 5$ is -3.
   • Therefore, $g(5) = -3$.

Final Answers:

• $f(g(2)) = 1$
• $g(f(4)) = 2$
• $f(1) = 2$
• $g(5) = -3$

Would you like more details on any of these steps or have further questions?

Here are 5 related questions to further your understanding:

1. How do you determine the domain and range of $f(x)$ and $g(x)$ from the graphs?
2. What is the composition of functions and how does it apply to real-world situations?
3. How do you find the inverse of a function using its graph?
4. Can you describe a situation where evaluating a composition of functions might be useful?
5. What changes in the graph would affect the results of $f(g(2))$ or $g(f(4))$?

Tip: When evaluating compositions of functions graphically, always start with the inner function and carefully trace the corresponding value on the outer function’s graph.