Math / Algebra

QuestionUse the selected values of a linear function $g(x)$ in the table and the equation $h(x)$ shown below to evaluate $(g \circ h)(-3)$ . \begin{tabular}{|c|c|} \hline $x$ & $g(x)$ \\ \hline-3 & -5 \\ \hline-1 & -1 \\ \hline 0 & 1 \\ \hline 4 & 9 \\ \hline \end{tabular} $h(x)=x^{2}-2$

Studdy Solution

STEP 1

1. We have a linear function $g(x)$ defined by specific values in a table.
2. We have a function $h(x) = x^2 - 2$ .
3. We need to evaluate the composition $(g \circ h)(-3)$ .

STEP 2

1. Evaluate $h(-3)$ .
2. Use the result from Step 1 to find $g(h(-3))$ using the table.

STEP 3

Substitute $x = -3$ into $h(x)$ :
$h(-3) = (-3)^2 - 2$

STEP 4

Simplify the expression:
$h(-3) = 9 - 2$ $h(-3) = 7$

STEP 5

Now, we need to evaluate $g(h(-3)) = g(7)$ .
Check the table for the value of $g(7)$ .

STEP 6

Since the value $x = 7$ is not in the table, we cannot directly evaluate $g(7)$ using the given table.
Since $g(7)$ is not available in the table, we cannot determine $(g \circ h)(-3)$ with the given information.

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QuestionUse the selected values of a linear function $g(x)$ in the table and the equation $h(x)$ shown below to evaluate $(g \circ h)(-3)$ . \begin{tabular}{|c|c|} \hline $x$ & $g(x)$ \\ \hline-3 & -5 \\ \hline-1 & -1 \\ \hline 0 & 1 \\ \hline 4 & 9 \\ \hline \end{tabular} $h(x)=x^{2}-2$

Studdy Solution

STEP 1

1. We have a linear function $g(x)$ defined by specific values in a table.
2. We have a function $h(x) = x^2 - 2$ .
3. We need to evaluate the composition $(g \circ h)(-3)$ .

STEP 2

1. Evaluate $h(-3)$ .
2. Use the result from Step 1 to find $g(h(-3))$ using the table.

STEP 3

Substitute $x = -3$ into $h(x)$ :
$h(-3) = (-3)^2 - 2$

STEP 4

Simplify the expression:
$h(-3) = 9 - 2$ $h(-3) = 7$

STEP 5

Now, we need to evaluate $g(h(-3)) = g(7)$ .
Check the table for the value of $g(7)$ .

STEP 6

Since the value $x = 7$ is not in the table, we cannot directly evaluate $g(7)$ using the given table.
Since $g(7)$ is not available in the table, we cannot determine $(g \circ h)(-3)$ with the given information.

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Studdy Solution

STEP 1

1. We have a linear function g(x) g(x) g(x) defined by specific values in a table.2. We have a function h(x)=x2−2 h(x) = x^2 - 2 h(x)=x2−2.3. We need to evaluate the composition (g∘h)(−3)(g \circ h)(-3)(g∘h)(−3).

STEP 2

1. Evaluate h(−3) h(-3) h(−3).2. Use the result from Step 1 to find g(h(−3)) g(h(-3)) g(h(−3)) using the table.

STEP 3

Substitute x=−3 x = -3 x=−3 into h(x) h(x) h(x):h(−3)=(−3)2−2 h(-3) = (-3)^2 - 2 h(−3)=(−3)2−2

STEP 4

Simplify the expression:h(−3)=9−2 h(-3) = 9 - 2 h(−3)=9−2 h(−3)=7 h(-3) = 7 h(−3)=7

STEP 5

Now, we need to evaluate g(h(−3))=g(7) g(h(-3)) = g(7) g(h(−3))=g(7).Check the table for the value of g(7) g(7) g(7).

STEP 6

Since the value x=7 x = 7 x=7 is not in the table, we cannot directly evaluate g(7) g(7) g(7) using the given table. Since g(7) g(7) g(7) is not available in the table, we cannot determine (g∘h)(−3)(g \circ h)(-3)(g∘h)(−3) with the given information.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. We have a linear function $g(x)$ defined by specific values in a table.
2. We have a function $h(x) = x^2 - 2$ .
3. We need to evaluate the composition $(g \circ h)(-3)$ .

1. Evaluate $h(-3)$ .
2. Use the result from Step 1 to find $g(h(-3))$ using the table.

Substitute $x = -3$ into $h(x)$ :
$h(-3) = (-3)^2 - 2$

Simplify the expression:
$h(-3) = 9 - 2$ $h(-3) = 7$

Now, we need to evaluate $g(h(-3)) = g(7)$ .
Check the table for the value of $g(7)$ .

Since the value $x = 7$ is not in the table, we cannot directly evaluate $g(7)$ using the given table.
Since $g(7)$ is not available in the table, we cannot determine $(g \circ h)(-3)$ with the given information.