To solve these problems, we need to evaluate the composition of functions $f$ and $g$ based on the graphs provided.

(a) $(f \circ g)(4)$

This means we first evaluate $g(4)$, and then use that result as the input for the function $f$.

1. From the graph of $g(x)$, locate the point where $x = 4$ and find $g(4)$. Based on the graph, $g(4) = 0$.
2. Now use $g(4) = 0$ as the input to $f$. From the graph of $f(x)$, locate $f(0)$. According to the graph, $f(0) = 4$.

Thus, $(f \circ g)(4) = f(g(4)) = f(0) = 4$.

(b) $(g \circ f)(1)$

This means we first evaluate $f(1)$, and then use that result as the input for the function $g$.

1. From the graph of $f(x)$, locate the point where $x = 1$ and find $f(1)$. Based on the graph, $f(1) = 2$.
2. Now use $f(1) = 2$ as the input to $g$. From the graph of $g(x)$, locate $g(2)$. According to the graph, $g(2) = 2$.

Thus, $(g \circ f)(1) = g(f(1)) = g(2) = 2$.

Final Answers:

• (a) $(f \circ g)(4) = 4$
• (b) $(g \circ f)(1) = 2$

Would you like further details or clarifications?

Here are 5 related questions for further practice:

1. What is $(f \circ g)(3)$?
2. Evaluate $(g \circ f)(2)$.
3. Determine $f(g(2))$.
4. What is $g(f(4))$?
5. Evaluate $f(g(1))$.

Tip: When working with function compositions, always evaluate the inner function first and use that result for the outer function.