The question asks you to use the graphs of $f(x)$ (in blue) and $g(x)$ (in red) to find the following values:

1. $f(g(3))$
2. $g(f(1))$
3. $g(g(10))$

Let's walk through the process to solve these.

1. $f(g(3))$

• Step 1: Find $g(3)$ from the graph of $g(x)$ (the red graph).

  • Look at the red graph at $x = 3$. From the image, it seems that $g(3) = 8$.

• Step 2: Now find $f(8)$ from the graph of $f(x)$ (the blue graph).

  • Look at the blue graph at $x = 8$. The value of $f(8)$ appears to be approximately $0$.

So, $f(g(3)) = f(8) = 0$.

2. $g(f(1))$

• Step 1: Find $f(1)$ from the graph of $f(x)$.

  • Look at the blue graph at $x = 1$. The value of $f(1) = 3$.

• Step 2: Now find $g(3)$ from the red graph.

  • From earlier, we know that $g(3) = 8$.

So, $g(f(1)) = g(3) = 8$.

3. $g(g(10))$

• Step 1: Find $g(10)$ from the red graph.

  • Look at the red graph at $x = 10$. The value of $g(10) = 12$.

• Step 2: Now find $g(12)$ from the red graph.

  • Look at the red graph at $x = 12$. The value of $g(12) = 0$.

So, $g(g(10)) = g(12) = 0$.

Summary of results:

1. $f(g(3)) = 0$
2. $g(f(1)) = 8$
3. $g(g(10)) = 0$

Let me know if you'd like more details or clarifications!

Here are 5 questions to extend your understanding:

1. What would $f(f(5))$ be using the same graphs?
2. How does the behavior of $f(x)$ differ from $g(x)$ over the interval $[0, 10]$?
3. Can you identify any points where both $f(x)$ and $g(x)$ share the same value for different $x$-values?
4. How would the result change if $f(x)$ or $g(x)$ were shifted up or down?
5. What is the domain and range of both $f(x)$ and $g(x)$ based on the graphs?

Tip: Always ensure that you read graphs carefully, as slight changes in values can lead to significant differences in results.