From the provided image, we have two graphs representing functions $f(x)$ and $g(x)$. We need to compute the following:

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

Let's break these down step by step using the graphs:

(a) $g(f(1))$:

1. First, find $f(1)$ from the graph of $f(x)$.
   • Looking at the graph, when $x = 1$, $f(1) = 3$.
2. Now, substitute $f(1) = 3$ into $g(x)$, i.e., find $g(3)$.
   • From the graph of $g(x)$, when $x = 3$, $g(3) = -2$.

Thus, $g(f(1)) = g(3) = -2$.

(b) $f(g(2))$:

1. First, find $g(2)$ from the graph of $g(x)$.
   • From the graph, when $x = 2$, $g(2) = 0$.
2. Now, substitute $g(2) = 0$ into $f(x)$, i.e., find $f(0)$.
   • From the graph of $f(x)$, when $x = 0$, $f(0) = 5$.

Thus, $f(g(2)) = f(0) = 5$.

Final Results:

• $g(f(1)) = -2$
• $f(g(2)) = 5$

Would you like further details or explanations? Here are five related questions to deepen understanding:

1. How do we interpret function composition when given two graphs?
2. What is the domain and range of the given functions $f$ and $g$?
3. How would $f(g(x))$ change if we changed the graph's scale?
4. What are some applications of function composition in real-world problems?
5. Could you solve $g(f(x))$ for other values of $x$?

Tip: Always check the axes' scales carefully when interpreting graphs to avoid mistakes in reading values.