Let's go through the problem step-by-step, using the graphs of $f(x)$ and $g(x)$.

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

   • First, find $g(1)$ from the graph of $g(x)$. At $x = 1$, the value of $g(1)$ is 0 (from the graph of $g(x)$).
   • Now, substitute $g(1) = 0$ into $f(x)$, so we need to find $f(0)$.
   • From the graph of $f(x)$, at $x = 0$, $f(0) = 3$.

   Therefore, $f(g(1)) = 3$.

2. For $g(f(3))$:

   • First, find $f(3)$ from the graph of $f(x)$. At $x = 3$, the value of $f(3)$ is 4.
   • Now, substitute $f(3) = 4$ into $g(x)$, so we need to find $g(4)$.
   • From the graph of $g(x)$, at $x = 4$, ( g(4) = 3 \