Problem
Evaluate each expression using the values given in the table. \begin{tabular}{|l|rrrrrrr|} \hline$x$ & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ $f(x)$ & 8 & 7 & 6 & 5 & 4 & 3 & 2 \\ $g(x)$ & -7 & -2 & 0 & 2 & 0 & -2 & -7 \\ \hline \end{tabular} a. $(f \circ g)(1)$ b. $(f \circ g)(2)$ d. $(g \circ f)(3)$ e. $(g \circ g)(1)$ c. $(g \circ f)(2)$ f. $(f \circ f)(3)$ a. $(f \circ g)(1)=5$ b. $(f \circ g)(2)=7$ c. $(g \circ f)(2)=$
Solution
Step 1 ：The question asks for the value of \((g \circ f)(2)\). This means we need to find the value of \(f(2)\) first, then substitute that value into \(g(x)\).
Step 2 ：From the table, we can see that \(f(2) = 3\). So we need to find the value of \(g(3)\).
Step 3 ：Looking at the table, we find that \(g(3) = -7\).
Step 4 ：Substituting \(f(2)\) into \(g(x)\), we get \(g(3) = -7\).
Step 5 ：Final Answer: \((g \circ f)(2) = \boxed{-7}\)
