We are given four functions: $f(x)$ is represented graphically, $g(x)$ is given as a set of ordered pairs, $h(x) = -x + 1$, and $p(t)$ is given in a table. We need to evaluate the following composite functions: $f(g(-4))$ $g(h(2))$ $p(f(-1))$ $g(p(-2))$

1. Problem Description

We are given four functions: $f(x)$ is represented graphically, $g(x)$ is given as a set of ordered pairs, $h(x) = -x + 1$, and $p(t)$ is given in a table. We need to evaluate the following composite functions:

$f(g(-4))$

$g(h(2))$

$p(f(-1))$

$g(p(-2))$

2. Solution Steps

First, we find $g(-4)$. From the definition of $g(x)$, we see that $g(-4) = -1$.

Then $f(g(-4)) = f(-1)$. From the graph of $f(x)$, we have $f(-1) = 5$.

Next, we find $h(2)$. We have $h(x) = -x + 1$, so $h(2) = -2 + 1 = -1$.

Then $g(h(2)) = g(-1)$. From the definition of $g(x)$, we see that $g(-1) = -3$.

Next, we find $f(-1)$. From the graph of $f(x)$, we have $f(-1) = 5$.

Then $p(f(-1)) = p(5)$. From the table of $p(t)$, we have $p(5) = 0$.

Finally, we find $p(-2)$. From the table of $p(t)$, we have $p(-2) = 3$.

Then $g(p(-2)) = g(3)$. From the definition of $g(x)$, we see that $g(3) = 2$.

3. Final Answer

$f(g(-4)) = 5$

$g(h(2)) = -3$

$p(f(-1)) = 0$

$g(p(-2)) = 2$