Let's evaluate the expressions using the graphs provided in the image.

1. $f(g(4))$:

• First, find $g(4)$ using the $g(x)$ graph (the one on the right).
  • For $x = 4$, $g(4) = 2$.
• Now, find $f(2)$ using the $f(x)$ graph (the one on the left).
  • For $x = 2$, $f(2) = 4$.
• So, $f(g(4)) = 4$.

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

• First, find $f(1)$ using the $f(x)$ graph.
  • For $x = 1$, $f(1) = 2$.
• Now, find $g(2)$ using the $g(x)$ graph.
  • For $x = 2$, $g(2) = 4$.
• So, $g(f(1)) = 4$.

3. $f(f(0))$:

• First, find $f(0)$ using the $f(x)$ graph.
  • For $x = 0$, $f(0) = 3$.
• Now, find $f(3)$ using the $f(x)$ graph.
  • For $x = 3$, $f(3) = 0$.
• So, $f(f(0)) = 0$.

4. $g(g(1))$:

• First, find $g(1)$ using the $g(x)$ graph.
  • For $x = 1$, $g(1) = 3$.
• Now, find $g(3)$ using the $g(x)$ graph.
  • For $x = 3$, $g(3) = 0$.
• So, $g(g(1)) = 0$.

Final Answers:

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

Would you like more details or have any questions?

Here are some related questions for further practice:

1. What is $f(g(2))$?
2. How do you find $g(f(3))$ using the graphs?
3. If $f(x)$ and $g(x)$ were swapped, how would the answers change?
4. How can we determine if $f(x)$ and $g(x)$ are one-to-one functions?
5. What is the significance of the intersections of the graphs with the axes?

Tip: When dealing with composite functions like $f(g(x))$, always solve the inner function first before moving on to the outer function.