Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To solve this problem, we need to find the value of [tex]\( x \)[/tex] such that [tex]\((f \circ g)(x) = -8\)[/tex]. The composite function [tex]\( (f \circ g)(x) \)[/tex] means [tex]\( f(g(x)) \)[/tex].
Given the values for [tex]\( f(x) \)[/tex]:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & -4 & -2 & 0 & 8 \\ \hline f(x) & -8 & -2 & 4 & 32 \\ \hline \end{array} \][/tex]
And the values for [tex]\( g(x) \)[/tex]:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 \\ \hline g(x) & -1 & -2 & -2 & -4 & -8 \\ \hline \end{array} \][/tex]
We need to find [tex]\( x \)[/tex] such that [tex]\( f(g(x)) = -8 \)[/tex]. Let's examine each available [tex]\( x \)[/tex] to see if [tex]\( f(g(x)) = -8 \)[/tex].
1. For [tex]\( x = 1 \)[/tex]:
[tex]\[ g(1) = -1 \quad \text{(from the table of } g(x) \text{)} \][/tex]
Since [tex]\( g(1) = -1 \)[/tex], we need to see if [tex]\( f(-1) = -8 \)[/tex]. However, [tex]\(-1\)[/tex] is not in the domain of [tex]\( f(x) \)[/tex] provided in the table.
2. For [tex]\( x = 2 \)[/tex]:
[tex]\[ g(2) = -2 \quad \text{(from the table of } g(x) \text{)} \][/tex]
Since [tex]\( g(2) = -2 \)[/tex], we need to see if [tex]\( f(-2) = -8 \)[/tex]. From the values given:
[tex]\[ f(-2) = -2 \quad (\text{not } -8) \][/tex]
3. For [tex]\( x = 3 \)[/tex]:
[tex]\[ g(3) = -2 \quad \text{(from the table of } g(x) \text{)} \][/tex]
Again, if [tex]\( g(3) = -2 \)[/tex], we need to see if [tex]\( f(-2) = -8 \)[/tex]. From the values given:
[tex]\[ f(-2) = -2 \quad (\text{not } -8) \][/tex]
4. For [tex]\( x = 4 \)[/tex]:
[tex]\[ g(4) = -4 \quad \text{(from the table of } g(x) \text{)} \][/tex]
Since [tex]\( g(4) = -4 \)[/tex], we need to see if [tex]\( f(-4) = -8 \)[/tex]. From the values given:
[tex]\[ f(-4) = -8 \][/tex]
This is the desired result, therefore:
[tex]\[ f(g(4)) = -8. \][/tex]
So, the value of [tex]\( x \)[/tex] when [tex]\((f \circ g)(x) = -8\)[/tex] is [tex]\( x = 4 \)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{4} \][/tex]
Given the values for [tex]\( f(x) \)[/tex]:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & -4 & -2 & 0 & 8 \\ \hline f(x) & -8 & -2 & 4 & 32 \\ \hline \end{array} \][/tex]
And the values for [tex]\( g(x) \)[/tex]:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 \\ \hline g(x) & -1 & -2 & -2 & -4 & -8 \\ \hline \end{array} \][/tex]
We need to find [tex]\( x \)[/tex] such that [tex]\( f(g(x)) = -8 \)[/tex]. Let's examine each available [tex]\( x \)[/tex] to see if [tex]\( f(g(x)) = -8 \)[/tex].
1. For [tex]\( x = 1 \)[/tex]:
[tex]\[ g(1) = -1 \quad \text{(from the table of } g(x) \text{)} \][/tex]
Since [tex]\( g(1) = -1 \)[/tex], we need to see if [tex]\( f(-1) = -8 \)[/tex]. However, [tex]\(-1\)[/tex] is not in the domain of [tex]\( f(x) \)[/tex] provided in the table.
2. For [tex]\( x = 2 \)[/tex]:
[tex]\[ g(2) = -2 \quad \text{(from the table of } g(x) \text{)} \][/tex]
Since [tex]\( g(2) = -2 \)[/tex], we need to see if [tex]\( f(-2) = -8 \)[/tex]. From the values given:
[tex]\[ f(-2) = -2 \quad (\text{not } -8) \][/tex]
3. For [tex]\( x = 3 \)[/tex]:
[tex]\[ g(3) = -2 \quad \text{(from the table of } g(x) \text{)} \][/tex]
Again, if [tex]\( g(3) = -2 \)[/tex], we need to see if [tex]\( f(-2) = -8 \)[/tex]. From the values given:
[tex]\[ f(-2) = -2 \quad (\text{not } -8) \][/tex]
4. For [tex]\( x = 4 \)[/tex]:
[tex]\[ g(4) = -4 \quad \text{(from the table of } g(x) \text{)} \][/tex]
Since [tex]\( g(4) = -4 \)[/tex], we need to see if [tex]\( f(-4) = -8 \)[/tex]. From the values given:
[tex]\[ f(-4) = -8 \][/tex]
This is the desired result, therefore:
[tex]\[ f(g(4)) = -8. \][/tex]
So, the value of [tex]\( x \)[/tex] when [tex]\((f \circ g)(x) = -8\)[/tex] is [tex]\( x = 4 \)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{4} \][/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.