Questions: The functions f and g are defined by the following tables. Use the tables to evaluate the given composite function. f(g(9)) x f(x) - ---- 2 -2 4 0 5 1 -2 7 x g(x) - ---- -2 0 2 -4 5 2 9 4 f(g(9))=

The functions f and g are defined by the following tables. Use the tables to evaluate the given composite function. f(g(9)) x f(x) - ---- 2 -2 4 0 5 1 -2 7 x g(x) - ---- -2 0 2 -4 5 2 9 4 f(g(9))=
Transcript text: The functions $f$ and $g$ are defined by the following tables. Use the tables to evaluate the given composite function. \[ f(g(9)) \] \begin{tabular}{|c|c|} \hline$x$ & $f(x)$ \\ \hline 2 & -2 \\ \hline 4 & 0 \\ \hline 5 & 1 \\ \hline-2 & 7 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline $\mathbf{x}$ & $\mathbf{g}(\mathbf{x})$ \\ \hline-2 & 0 \\ \hline 2 & -4 \\ \hline 5 & 2 \\ \hline 9 & 4 \\ \hline \end{tabular} \[ f(g(9))= \] $\square$
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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 f(g(x)). Given input value $x = 9$, 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 $x = 9$ is 0.

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