Answer: h(g(h(3))) = -2
Find:
[tex]h(g(h(3)))[/tex]
First, we will find the value of h(3). Based on the graph, if x=3, h(x) = -1:
We now have:
[tex]\begin{gathered} h(g(h(3))) \\ \Rightarrow h(g(-1)) \end{gathered}[/tex]
Now, we need to find g(-1). Looking at the table, we see that g(-1) = 0:
We now have:
[tex]\begin{gathered} h(g(-1)) \\ \Rightarrow h(0) \end{gathered}[/tex]
We then need to look at the graph again to find h(0):
With this, we know that:
[tex]\begin{gathered} h(g(h(3))) \\ \Rightarrow h(g(-1)) \\ \Rightarrow h(0)=-2 \end{gathered}[/tex]
Therefore, h(g(h(3))) = -2
