We are tasked with evaluating $f(g(2))$, using the given graphs of the functions $f(x)$ and $g(x)$.

Step 1: Find $g(2)$

From the graph of $g(x)$ (the blue curve), we observe the value of $g$ at $x = 2$.

• Locate $x = 2$ on the horizontal axis.
• From the graph, the value of $g(2)$ is approximately 0.

So, $g(2) = 0$.

Step 2: Find $f(g(2)) = f(0)$

Now, we need to find $f(0)$ using the graph of $f(x)$ (the red line).

• Locate $x = 0$ on the horizontal axis.
• From the graph, the value of $f(0)$ is 2.

Therefore, $f(g(2)) = f(0) = 2$.

Final Answer:

$f(g(2)) = 2$.

Would you like further explanation or details on this? Here are some related questions you might find useful:

1. How do we evaluate nested functions using graphs?
2. What are some common mistakes when interpreting graphs?
3. How can we interpret the behavior of $f(x)$ for values near $x = 0$?
4. What is the significance of function composition in calculus?
5. How do transformations affect the graph of a function?

Tip: When evaluating composite functions graphically, always start from the inner function and use its output as the input for the outer function.