Questions: Given the following table of values, compute (f ∘ g)(3). x -1 1 3 5 7 9 f(x) -19 12 3 -4 -18 -17 g(x) 13 2 1 -4 -1 3

Transcript text: Given the following table of values, compute $(f \circ g)(3)$. \begin{tabular}{ccccccc} $x$ & -1 & 1 & 3 & 5 & 7 & 9 \\ \hline$f(x)$ & -19 & 12 & 3 & -4 & -18 & -17 \\ \hline$g(x)$ & 13 & 2 & 1 & -4 & -1 & 3 \\ \hline \end{tabular}

Solution

Solution Steps

To compute $(f \circ g)(3)$, we need to first find $g(3)$ using the table, and then use this result to find $f(g(3))$. Specifically, we will:

Look up the value of $g(3)$ in the table.
Use the result from step 1 to find $f(g(3))$ by looking up the corresponding value in the table for $f(x)$.

Step 1: Determine $ g(3) $

To find $ (f \circ g)(3) $, we first need to determine $ g(3) $ from the given table. According to the table, $ g(3) = 1 $.

Step 2: Compute $ f(g(3)) $

With $ g(3) = 1 $, we now need to find $ f(1) $. From the table, we see that $ f(1) = 12 $.

Final Answer

Thus, the value of $ (f \circ g)(3) $ is $\boxed{12}$.

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