Question

homework 16: section 3.4
score: 40/160 answered: 4/16
question 4
use the table below to find:
$(f \circ g)(7) = \square$ $(g \circ f)(-9) = \square$
$(f \circ f)(14) = \square$ $(g \circ g)(10) = \square$
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$$\begin{tabular}{|c|c|c|c|c|c|c|c|c|} \\hline $x$ & -9 & -6 & 4 & 5 & 6 & 7 & 10 & 14 \\\\ \\hline $f(x)$ & 14 & 7 & -6 & 10 & 5 & 4 & -9 & 6 \\\\ \\hline $g(x)$ & -6 & 7 & 10 & -9 & 5 & 14 & 4 & 6 \\\\ \\hline \\end{tabular}$$

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Explanation:

Step1: Find \((f \circ g)(7)\)

First, recall that \((f \circ g)(7)=f(g(7))\). From the table, when \(x = 7\), \(g(7)=14\). Then we need to find \(f(14)\). Looking at the table, when \(x = 14\), \(f(14)=6\). So \((f \circ g)(7)=f(g(7)) = f(14)=6\).

Step2: Find \((g \circ f)(-9)\)

Recall that \((g \circ f)(-9)=g(f(-9))\). From the table, when \(x=-9\), \(f(-9) = 14\). Then we need to find \(g(14)\). Looking at the table, when \(x = 14\), \(g(14)=6\). So \((g \circ f)(-9)=g(f(-9))=g(14) = 6\).

Step3: Find \((f \circ f)(14)\)

Recall that \((f \circ f)(14)=f(f(14))\). From the table, when \(x = 14\), \(f(14)=6\). Then we need to find \(f(6)\). Looking at the table, when \(x = 6\), \(f(6)=5\). So \((f \circ f)(14)=f(f(14))=f(6)=5\).

Step4: Find \((g \circ g)(10)\)

Recall that \((g \circ g)(10)=g(g(10))\). From the table, when \(x = 10\), \(g(10)=4\). Then we need to find \(g(4)\). Looking at the table, when \(x = 4\), \(g(4)=10\). So \((g \circ g)(10)=g(g(10))=g(4)=10\).

Answer:

\((f \circ g)(7)=\boxed{6}\)
\((g \circ f)(-9)=\boxed{6}\)
\((f \circ f)(14)=\boxed{5}\)
\((g \circ g)(10)=\boxed{10}\)