Problem

Use the tables to evaluate the expression $(g \circ f)(3)$. \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline$x$ & 1 & 3 & & 6 & $x$ & 1 & 3 & & 6 \\ \hline$f(x)$ & 4 & 6 & 1 & 3 & $g(x)$ & 3 & & & 7 \\ \hline \end{tabular} \[ (g \circ f)(3)=\square \]

Solution

Step 1 :The expression $(g \circ f)(3)$ represents the composition of two functions, $g$ and $f$.

Step 2 :To evaluate this expression, we first find the value of $f(3)$ from the table, which is 6.

Step 3 :We then substitute this value into $g(x)$, so we need to find the value of $g(6)$ from the table, which is 7.

Step 4 :So, $(g \circ f)(3)=g(f(3))=g(6)=7$

Step 5 :Final Answer: $(g \circ f)(3)=\boxed{7}$

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Source: https://solvelyapp.com/problems/bTaZau6Kf0/

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