Let's solve the given questions step by step by analyzing the graphs of the functions $f(x)$ and $g(x)$:

1. $f(g(5))$

• First, find $g(5)$ from the graph of $g(x)$.
  • On the graph of $g(x)$, when $x = 5$, $g(5) = 4$.
• Now, find $f(4)$ from the graph of $f(x)$.
  • On the graph of $f(x)$, when $x = 4$, $f(4) = 0$.
• So, $f(g(5)) = f(4) = 0$.

2. $g(f(1))$

• First, find $f(1)$ from the graph of $f(x)$.
  • On the graph of $f(x)$, when $x = 1$, $f(1) = 2$.
• Now, find $g(2)$ from the graph of $g(x)$.
  • On the graph of $g(x)$, when $x = 2$, $g(2) = 0$.
• So, $g(f(1)) = g(2) = 0$.

3. $f(f(4))$

• First, find $f(4)$ from the graph of $f(x)$.
  • On the graph of $f(x)$, when $x = 4$, $f(4) = 0$.
• Now, find $f(0)$ from the graph of $f(x)$.
  • On the graph of $f(x)$, when $x = 0$, $f(0) = 1$.
• So, $f(f(4)) = f(0) = 1$.

4. $g(g(2))$

• First, find $g(2)$ from the graph of $g(x)$.
  • On the graph of $g(x)$, when $x = 2$, $g(2) = 0$.
• Now, find $g(0)$ from the graph of $g(x)$.
  • On the graph of $g(x)$, when $x = 0$, $g(0) = 1$.
• So, $g(g(2)) = g(0) = 1$.

Final Answers:

1. $f(g(5)) = 0$
2. $g(f(1)) = 0$
3. $f(f(4)) = 1$
4. $g(g(2)) = 1$

Would you like more details on any of the steps?

Here are some related questions for further practice:

1. What is $g(f(5))$?
2. What is $f(g(4))$?
3. What is $f(f(3))$?
4. What is $g(f(2))$?
5. What is $f(g(3))$?

Tip: Always start by evaluating the innermost function when dealing with compositions of functions.