IDNLearn.com provides a collaborative environment for finding and sharing answers. Find reliable solutions to your questions quickly and accurately with help from our dedicated community of experts.
Sagot :
Let's go through the problem one step at a time.
#### Given Information:
- Function [tex]\( f(x) = -2x + 5 \)[/tex]
- Values of function [tex]\( g(x) \)[/tex]:
[tex]\[ \begin{array}{|c|c|} \hline x & g(x) \\ \hline -2 & 6 \\ \hline 0 & 1 \\ \hline 1 & -2 \\ \hline 4 & 7 \\ \hline 6 & 10 \\ \hline 7 & 6 \\ \hline \end{array} \][/tex]
Information about [tex]\( h(x) \)[/tex] is not provided, so we’ll answer the questions requiring this function based on the given data only.
#### 1) What is the value of [tex]\( f(4) \)[/tex]?
To find [tex]\( f(4) \)[/tex], substitute [tex]\( x = 4 \)[/tex] into [tex]\( f(x) \)[/tex]:
[tex]\[ f(4) = -2(4) + 5 = -8 + 5 = -3 \][/tex]
Answer: [tex]\( f(4) = -3 \)[/tex]
#### 2) What is the value of [tex]\( g(4) \)[/tex]?
From the table provided, when [tex]\( x = 4 \)[/tex]:
[tex]\[ g(4) = 7 \][/tex]
Answer: [tex]\( g(4) = 7 \)[/tex]
#### 3) What is the value of [tex]\( h(4) \)[/tex]?
Insufficient information about the function [tex]\( h \)[/tex] is provided, so we cannot determine [tex]\( h(4) \)[/tex].
Answer: Information about [tex]\( h(x) \)[/tex] is not provided.
#### 4-5) For what values of [tex]\( x \)[/tex] is [tex]\( f(x)=13 \)[/tex], [tex]\( g(x)=6 \)[/tex], [tex]\( h(x)=1 \)[/tex]?
##### 4) For what values of [tex]\( x \)[/tex] is [tex]\( f(x)=13 \)[/tex]?
To solve, set [tex]\( f(x) = 13 \)[/tex]:
[tex]\[ -2x + 5 = 13 \][/tex]
Subtracting 5 from both sides:
[tex]\[ -2x = 8 \][/tex]
Dividing both sides by -2:
[tex]\[ x = -4 \][/tex]
Answer: [tex]\( x = -4 \)[/tex]
##### 5) For what values of [tex]\( x \)[/tex] is [tex]\( g(x)=6 \)[/tex]?
From the table, [tex]\( g(x) = 6 \)[/tex] for [tex]\( x = -2 \)[/tex] and [tex]\( x = 7 \)[/tex].
Answer: [tex]\( x = -2 \)[/tex] or [tex]\( x = 7 \)[/tex]
##### 6) For what values of [tex]\( x \)[/tex] is [tex]\( h(x)=1 \)[/tex]?
Insufficient information about the function [tex]\( h \)[/tex] is provided, so we cannot determine values of [tex]\( x \)[/tex] for which [tex]\( h(x) = 1 \)[/tex].
Answer: Information about [tex]\( h(x) \)[/tex] is not provided.
#### 7) What is the value of [tex]\( f(2) + g(7) + h(0) \)[/tex]?
Given [tex]\( h(0) \)[/tex] cannot be determined without information about [tex]\( h \)[/tex]. Hence, it's not possible to solve this part accurately.
Answer: Information about [tex]\( h(x) \)[/tex] is not provided.
#### 8) What is the value of [tex]\( f(g(0)) \)[/tex]?
First, find [tex]\( g(0) \)[/tex]:
[tex]\[ g(0) = 1 \][/tex]
Next, find [tex]\( f(g(0)) = f(1) \)[/tex]:
[tex]\[ f(1) = -2(1) + 5 = -2 + 5 = 3 \][/tex]
Answer: [tex]\( f(g(0)) = 3 \)[/tex]
#### 9) What is the value of [tex]\( h(f(0)) \)[/tex]?
First, find [tex]\( f(0) \)[/tex]:
[tex]\[ f(0) = -2(0) + 5 = 5 \][/tex]
Next, find [tex]\( h(f(0)) = h(5) \)[/tex], but insufficient information about function [tex]\( h \)[/tex] is provided.
Answer: Information about [tex]\( h(x) \)[/tex] is not provided.
#### 10) What is the value of [tex]\( f(h(g(-2))) \)[/tex]?
First, find [tex]\( g(-2) \)[/tex]:
[tex]\[ g(-2) = 6 \][/tex]
Next, find [tex]\( h(g(-2)) = h(6) \)[/tex], but insufficient information about [tex]\( h \)[/tex] is provided.
Answer: Information about [tex]\( h(x) \)[/tex] is not provided.
#### 11-14) Membership in the domain and range of [tex]\( h \)[/tex]
##### 11) Is the number 6 a member of the domain of function [tex]\( h \)[/tex]?
Insufficient information about the domain of [tex]\( h \)[/tex] is provided.
Answer: Information about the domain of [tex]\( h(x) \)[/tex] is not provided.
##### 12) Is the number -5.5 a member of the domain of function [tex]\( h \)[/tex]?
Insufficient information about the domain of [tex]\( h \)[/tex] is provided.
Answer: Information about the domain of [tex]\( h(x) \)[/tex] is not provided.
##### 13) Is the number 6 a member of the range of function [tex]\( h \)[/tex]?
Insufficient information about the range of [tex]\( h \)[/tex] is provided.
Answer: Information about the range of [tex]\( h(x) \)[/tex] is not provided.
##### 14) Is the number -5.5 a member of the range of function [tex]\( h \)[/tex]?
Insufficient information about the range of [tex]\( h \)[/tex] is provided.
Answer: Information about the range of [tex]\( h(x) \)[/tex] is not provided.
It's important to note that the lack of information about [tex]\( h \)[/tex] makes it impossible to accurately answer several questions. If additional information about [tex]\( h \)[/tex] is provided, these questions could be revisited.
#### Given Information:
- Function [tex]\( f(x) = -2x + 5 \)[/tex]
- Values of function [tex]\( g(x) \)[/tex]:
[tex]\[ \begin{array}{|c|c|} \hline x & g(x) \\ \hline -2 & 6 \\ \hline 0 & 1 \\ \hline 1 & -2 \\ \hline 4 & 7 \\ \hline 6 & 10 \\ \hline 7 & 6 \\ \hline \end{array} \][/tex]
Information about [tex]\( h(x) \)[/tex] is not provided, so we’ll answer the questions requiring this function based on the given data only.
#### 1) What is the value of [tex]\( f(4) \)[/tex]?
To find [tex]\( f(4) \)[/tex], substitute [tex]\( x = 4 \)[/tex] into [tex]\( f(x) \)[/tex]:
[tex]\[ f(4) = -2(4) + 5 = -8 + 5 = -3 \][/tex]
Answer: [tex]\( f(4) = -3 \)[/tex]
#### 2) What is the value of [tex]\( g(4) \)[/tex]?
From the table provided, when [tex]\( x = 4 \)[/tex]:
[tex]\[ g(4) = 7 \][/tex]
Answer: [tex]\( g(4) = 7 \)[/tex]
#### 3) What is the value of [tex]\( h(4) \)[/tex]?
Insufficient information about the function [tex]\( h \)[/tex] is provided, so we cannot determine [tex]\( h(4) \)[/tex].
Answer: Information about [tex]\( h(x) \)[/tex] is not provided.
#### 4-5) For what values of [tex]\( x \)[/tex] is [tex]\( f(x)=13 \)[/tex], [tex]\( g(x)=6 \)[/tex], [tex]\( h(x)=1 \)[/tex]?
##### 4) For what values of [tex]\( x \)[/tex] is [tex]\( f(x)=13 \)[/tex]?
To solve, set [tex]\( f(x) = 13 \)[/tex]:
[tex]\[ -2x + 5 = 13 \][/tex]
Subtracting 5 from both sides:
[tex]\[ -2x = 8 \][/tex]
Dividing both sides by -2:
[tex]\[ x = -4 \][/tex]
Answer: [tex]\( x = -4 \)[/tex]
##### 5) For what values of [tex]\( x \)[/tex] is [tex]\( g(x)=6 \)[/tex]?
From the table, [tex]\( g(x) = 6 \)[/tex] for [tex]\( x = -2 \)[/tex] and [tex]\( x = 7 \)[/tex].
Answer: [tex]\( x = -2 \)[/tex] or [tex]\( x = 7 \)[/tex]
##### 6) For what values of [tex]\( x \)[/tex] is [tex]\( h(x)=1 \)[/tex]?
Insufficient information about the function [tex]\( h \)[/tex] is provided, so we cannot determine values of [tex]\( x \)[/tex] for which [tex]\( h(x) = 1 \)[/tex].
Answer: Information about [tex]\( h(x) \)[/tex] is not provided.
#### 7) What is the value of [tex]\( f(2) + g(7) + h(0) \)[/tex]?
Given [tex]\( h(0) \)[/tex] cannot be determined without information about [tex]\( h \)[/tex]. Hence, it's not possible to solve this part accurately.
Answer: Information about [tex]\( h(x) \)[/tex] is not provided.
#### 8) What is the value of [tex]\( f(g(0)) \)[/tex]?
First, find [tex]\( g(0) \)[/tex]:
[tex]\[ g(0) = 1 \][/tex]
Next, find [tex]\( f(g(0)) = f(1) \)[/tex]:
[tex]\[ f(1) = -2(1) + 5 = -2 + 5 = 3 \][/tex]
Answer: [tex]\( f(g(0)) = 3 \)[/tex]
#### 9) What is the value of [tex]\( h(f(0)) \)[/tex]?
First, find [tex]\( f(0) \)[/tex]:
[tex]\[ f(0) = -2(0) + 5 = 5 \][/tex]
Next, find [tex]\( h(f(0)) = h(5) \)[/tex], but insufficient information about function [tex]\( h \)[/tex] is provided.
Answer: Information about [tex]\( h(x) \)[/tex] is not provided.
#### 10) What is the value of [tex]\( f(h(g(-2))) \)[/tex]?
First, find [tex]\( g(-2) \)[/tex]:
[tex]\[ g(-2) = 6 \][/tex]
Next, find [tex]\( h(g(-2)) = h(6) \)[/tex], but insufficient information about [tex]\( h \)[/tex] is provided.
Answer: Information about [tex]\( h(x) \)[/tex] is not provided.
#### 11-14) Membership in the domain and range of [tex]\( h \)[/tex]
##### 11) Is the number 6 a member of the domain of function [tex]\( h \)[/tex]?
Insufficient information about the domain of [tex]\( h \)[/tex] is provided.
Answer: Information about the domain of [tex]\( h(x) \)[/tex] is not provided.
##### 12) Is the number -5.5 a member of the domain of function [tex]\( h \)[/tex]?
Insufficient information about the domain of [tex]\( h \)[/tex] is provided.
Answer: Information about the domain of [tex]\( h(x) \)[/tex] is not provided.
##### 13) Is the number 6 a member of the range of function [tex]\( h \)[/tex]?
Insufficient information about the range of [tex]\( h \)[/tex] is provided.
Answer: Information about the range of [tex]\( h(x) \)[/tex] is not provided.
##### 14) Is the number -5.5 a member of the range of function [tex]\( h \)[/tex]?
Insufficient information about the range of [tex]\( h \)[/tex] is provided.
Answer: Information about the range of [tex]\( h(x) \)[/tex] is not provided.
It's important to note that the lack of information about [tex]\( h \)[/tex] makes it impossible to accurately answer several questions. If additional information about [tex]\( h \)[/tex] is provided, these questions could be revisited.
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. IDNLearn.com is dedicated to providing accurate answers. Thank you for visiting, and see you next time for more solutions.
