Problem

Use the tables to evaluate the expressions. \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline$x$ & 1 & 3 & 4 & 6 \\ \hline$f(x)$ & 4 & 6 & 1 & 3 \\ \hline$g(x)$ & 3 & 4 & 6 & 7 \\ \hline \end{tabular} Find $(g \circ f)(3)$. Select the correct choice below and fill in any answer boxes within your choice. A. $(g \circ f)(3)=\square$ B. The value is undefined.

Solution

Step 1 :The expression \((g \circ f)(3)\) represents the composition of the functions g and f at x=3. This means we first apply the function f to 3, and then apply the function g to the result.

Step 2 :From the table, we can see that \(f(3) = 6\).

Step 3 :Then we apply the function g to the result. From the table, we can see that \(g(6) = 7\).

Step 4 :So, \((g \circ f)(3) = 7\).

Step 5 :Therefore, the correct choice is A. \(\boxed{(g \circ f)(3)=7}\).

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