Given: the table:
x -3 -2 -1 0 1 2 3
f(x) 8 7 6 5 4 3 2
g(x) -7 -2 0 1 0 -2 -7
Let's solve for the following:
• (a). (f o g)(1)
To solve this function operation, we have:
(f o g)(1) = f(g(1))
Here we are to find the value of f when g(1).
Therefore, we have:
g(1) = 0
f(g(1)) = f(0) = 5
Hence, we have:
(f o g)(1) = 5
• (b). (f o g)(2)
Apply the formula:
(f o g)(x) = f(g(x))
Thus, we have:
(f o g)(2) = f(g(2))
From the table, we have:
g(2) = -2
f(g(2) = f(-2) = 7
Hence, we have:
(f o g)(2) = 7
• (c). (g o f)(2)
We have:
(g o f)(2) = g(f(2))
From the table, we have:
f(2) = 3
g(f(2)) = g(3) = -7
Thus we have:
(f o g)(2) = -7
• (d). (g o f)(3)
Apply the f