Looking at the provided graphs for $f(x)$ and $g(x)$, let's evaluate the required expressions step by step:

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

• From the graph of $f(x)$, at $x = 1$, the value of $f(1)$ is 4.
• From the graph of $g(x)$, at $x = 2$, the value of $g(2)$ is 5.

Thus, $f(1) + g(2) = 4 + 5 = 9$.

2. $f(1) \cdot g(5)$

• From the graph of $f(x)$, at $x = 1$, the value of $f(1)$ is 4.
• From the graph of $g(x)$, at $x = 5$, the value of $g(5)$ is 1.

Thus, $f(1) \cdot g(5) = 4 \cdot 1 = 4$.

3. $g(5) - f(4)$

• From the graph of $g(x)$, at $x = 5$, the value of $g(5)$ is 1.
• From the graph of $f(x)$, at $x = 4$, the value of $f(4)$ is 0.

Thus, $g(5) - f(4) = 1 - 0 = 1$.

4. $\frac{g(2)}{f(4)}$

• From the graph of $g(x)$, at $x = 2$, the value of $g(2)$ is 5.
• From the graph of $f(x)$, at $x = 4$, the value of $f(4)$ is 0.

Since division by zero is undefined, this expression cannot be evaluated.

Let me know if you'd like further details on any part. Here are five related questions to explore:

1. What is $f(2)$ and how does it relate to $g(3)$?
2. Can you find $f(3) \cdot g(4)$?
3. What would $g(1) + f(2)$ equal based on the graphs?
4. If $f(x)$ was a linear function, how would you represent its equation?
5. How do you find the inverse of $g(x)$ based on its graph?

Tip: Always check for points where a function touches the x-axis as it might lead to special cases in calculations.