Questions: The functions f and g are defined by the following tables. Use the tables to evaluate the given composite function. (g ◦ f)(-1) x f(x) -1 1 0 4 1 5 6 -1 x g(x) -1 -6 1 -3 5 2 9 -1 (g ◦ f)(-1)= □

The functions f and g are defined by the following tables. Use the tables to evaluate the given composite function.
(g ◦ f)(-1)

x  f(x)
-1  1
0  4
1  5
6  -1

x  g(x)
-1  -6
1  -3
5  2
9  -1

(g ◦ f)(-1)=
□
Transcript text: The functions f and g are defined by the following tables. Use the tables to evaluate the given composite function. \[ (g \circ f)(-1) \] \begin{tabular}{|c|c|} \hline$x$ & $f(x)$ \\ \hline-1 & 1 \\ \hline 0 & 4 \\ \hline 1 & 5 \\ \hline 6 & -1 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline$x$ & $g(x)$ \\ \hline-1 & -6 \\ \hline 1 & -3 \\ \hline 5 & 2 \\ \hline 9 & -1 \\ \hline \end{tabular} \[ (g \circ f)(-1)= \] $\square$
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Solution

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Solution Steps

Step 1: Identify the Composition Order and Locate the Initial Mapping

The composition order is (g \circ f)(x). Given input value $x = -1$, the initial mapping is found.

Step 2: Find the Next Mapping

The output from the inner function is used as the input to find the corresponding output in the outer function's table.

Final Answer: The result of the composite function for input $x = -1$ is -3.

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