The problem asks us to evaluate four composite functions, $f(g(-7))$, $g(f(-5))$, $f(f(14))$, and $g(g(-10))$, using the given table of values for the functions $f(x)$ and $g(x)$.

1. Problem Description

The problem asks us to evaluate four composite functions, $f(g(-7))$, $g(f(-5))$, $f(f(14))$, and $g(g(-10))$, using the given table of values for the functions $f(x)$ and $g(x)$.

2. Solution Steps

We will use the table to find the values of the inner functions first, and then use those values as inputs to the outer functions.

a) $f(g(-7))$:

First, find $g(-7)$. From the table, $g(-7) = 14$.

Then, find $f(14)$. From the table, $f(14) = -7$.

So, $f(g(-7)) = f(14) = -7$.

b) $g(f(-5))$:

First, find $f(-5)$. From the table, $f(-5) = 5$.

Then, find $g(5)$. From the table, $g(5) = -7$.

So, $g(f(-5)) = g(5) = -7$.

c) $f(f(14))$:

First, find $f(14)$. From the table, $f(14) = -7$.

Then, find $f(-7)$. From the table, $f(-7) = -10$.

So, $f(f(14)) = f(-7) = -10$.

d) $g(g(-10))$:

First, find $g(-10)$. From the table, $g(-10) = -10$.

Then, find $g(-10)$. From the table, $g(-10) = -10$.

So, $g(g(-10)) = g(-10) = -10$.

3. Final Answer

$f(g(-7)) = -7$

$g(f(-5)) = -7$

$f(f(14)) = -10$

$g(g(-10)) = -10$