To solve $f(g(2))$, we need to follow these steps:

Step 1: Evaluate $g(2)$

From the graph of $g(x)$, locate the point where $x = 2$. At $x = 2$, the value of $g(x)$ is the $y$-coordinate of the corresponding point on the curve. Looking at the graph, it appears that $g(2) = 4$.

Step 2: Evaluate $f(g(2)) = f(4)$

Now, we need to find $f(4)$. From the graph of $f(x)$, locate the point where $x = 4$. The value of $f(4)$ is the $y$-coordinate of that point. From the graph, it seems that $f(4) = 5$.

Final Answer:

So, $f(g(2)) = f(4) = 5$.

Would you like more details on this solution? Here are 5 related questions that can expand your understanding:

1. How would you find $f(g(-2))$ from the graph?
2. What happens if $g(x)$ returns a value where $f(x)$ is undefined?
3. How can you interpret function composition from graphs in general?
4. What is the meaning of the vertical and horizontal axis in function graphs like this?
5. Can a function have multiple values at a single input, and how does this affect composition?

Tip: Always check for points of discontinuity or undefined values in both functions before evaluating compositions.