Let's work through the problem one part at a time using the functions and tables provided in the image.

We have the following information:

1. Function $f(x)$ given as a set of pairs:

   • $f(x) = \{(0,1), (1,0), (2,5), (3,2), (4,3), (5,4)\}$ This is a lookup table, where for example, $f(0) = 1$, $f(1) = 0$, etc.

2. Function $g(x)$ represented as:

   • $g(x)$ is given as a table with $x$ and corresponding $y$ values:
   x & y \\ \hline -3 & -6 \\ -1 & 6 \\ 0 & 3 \\ 3 & 5 \\ 4 & 8 \\ 5 & 11 \\ 6 & 3 \\ \end{array}$$ For example, $$g(3) = 5$$, $$g(5) = 11$$, etc.

3. Function $h(x)$ defined as:

   • $h(x) = \sqrt{x - 2}$ This is a square root function, so to compute $h(x)$, we use this formula.

4. Function $j(x)$ is graphed. The graph provides a way to evaluate $j(x)$ by checking the corresponding $y$-value for a given $x$-value.

Let's now answer the questions one by one:

A. $h(g(5))$

First, we compute $g(5)$ using the table for $g(x)$.
From the table, $g(5) = 11$.

Next, compute $h(11)$ using the formula $h(x) = \sqrt{x - 2}$: $h(11) = \sqrt{11 - 2} = \sqrt{9} = 3$

So, $h(g(5)) = 3$.

B. $f(j(1))$

To solve this, we need to first find $j(1)$ from the graph of $j(x)$. Looking at the graph, when $x = 1$, $j(x) = 2$.

Next, we compute $f(2)$ using the set of pairs for $f(x)$. From the set, $f(2) = 5$.

So, $f(j(1)) = 5$.

C. $j(h(6))$

First, compute $h(6)$ using the formula $h(x) = \sqrt{x - 2}$: $h(6) = \sqrt{6 - 2} = \sqrt{4} = 2$

Now, use the graph to find $j(2)$. From the graph, when $x = 2$, $j(x) = 4$.

So, $j(h(6)) = 4$.

D. $g(f(3))$

First, compute $f(3)$ using the set of pairs for $f(x)$. From the set, $f(3) = 2$.

Next, compute $g(2)$ using the table for $g(x)$. Unfortunately, the table does not directly give $g(2)$. Based on this, we might infer that $g(2)$ isn't defined here, or we need more information.

Thus, $g(f(3))$ cannot be determined with the given information from the table.

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

1. What happens if $h(x)$ is undefined for certain inputs?
2. How does the graph of $j(x)$ help with interpreting the function's behavior?
3. Can you find $g(x)$ values through interpolation if they're missing from the table?
4. How does the square root function behave when $x < 2$?
5. What is the general approach to solving compositions of functions like these?

Tip: Always check if the input to a function lies within its domain to ensure you're not dealing with undefined values.