Given the functions: g(x) = |x-2| Evaluate the function (h-g) (5) for the given value of x. Write your answer as an integer or simplified fraction. Select "Undefined" if applicable. f(x) = 6x (h.g) (5) is. X Undefined S h(x) = x-4
Given the functions: g(x) = |x-2| Evaluate the function (h-g) (5) for the given value of x. Write your answer as an integer or simplified fraction. Select "Undefined" if applicable. f(x) = 6x (h.g) (5) is. X Undefined S h(x) = x-4
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.9: Combining Functions
Problem 52HP
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Question
![### Evaluating Composite Functions
Given the functions:
\[ f(x) = 6x \]
\[ g(x) = |x - 2| \]
\[ h(x) = \frac{1}{x - 4} \]
Evaluate the function \((h \cdot g)(5)\) for the given value of \( x \). Write your answer as an integer or a simplified fraction. Select "Undefined" if applicable.
\[
(h \cdot g)(5) \text{ is } \underline{\hspace{2cm}}
\]
Options:
- Checkbox labeled "Undefined"
- Text input field with an answer button labeled "X"
- Reset button labeled with a circular arrow](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F262a59b3-3740-48a2-981b-c8dd0f86c255%2F3d5c830e-028e-4ba6-a4fb-332b88cc2084%2Ffa13wop_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Evaluating Composite Functions
Given the functions:
\[ f(x) = 6x \]
\[ g(x) = |x - 2| \]
\[ h(x) = \frac{1}{x - 4} \]
Evaluate the function \((h \cdot g)(5)\) for the given value of \( x \). Write your answer as an integer or a simplified fraction. Select "Undefined" if applicable.
\[
(h \cdot g)(5) \text{ is } \underline{\hspace{2cm}}
\]
Options:
- Checkbox labeled "Undefined"
- Text input field with an answer button labeled "X"
- Reset button labeled with a circular arrow
![**Given the functions:**
\[ f(x) = 5x \]
\[ g(x) = |x - 6| \]
\[ h(x) = \frac{1}{x - 4} \]
Evaluate the function \(\left( \frac{h}{g} \right)(-6)\) for \(x = -6\). Write your answer as an integer or simplified fraction. Select "Undefined" if applicable.
**Solution:**
First, find \( g(-6) \):
\[ g(-6) = |-6 - 6| = |-12| = 12 \]
Next, find \( h(-6) \):
\[ h(-6) = \frac{1}{-6 - 4} = \frac{1}{-10} = -\frac{1}{10} \]
Now, evaluate \(\left( \frac{h}{g} \right)(-6)\):
\[ \left( \frac{h}{g} \right)(-6) = \frac{h(-6)}{g(-6)} = \frac{-\frac{1}{10}}{12} = \frac{-1}{10 \times 12} = \frac{-1}{120} \]
Therefore, \(\left( \frac{h}{g} \right)(-6)\) is:
\[ \boxed{-\frac{1}{120}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F262a59b3-3740-48a2-981b-c8dd0f86c255%2F3d5c830e-028e-4ba6-a4fb-332b88cc2084%2Fzdamfe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Given the functions:**
\[ f(x) = 5x \]
\[ g(x) = |x - 6| \]
\[ h(x) = \frac{1}{x - 4} \]
Evaluate the function \(\left( \frac{h}{g} \right)(-6)\) for \(x = -6\). Write your answer as an integer or simplified fraction. Select "Undefined" if applicable.
**Solution:**
First, find \( g(-6) \):
\[ g(-6) = |-6 - 6| = |-12| = 12 \]
Next, find \( h(-6) \):
\[ h(-6) = \frac{1}{-6 - 4} = \frac{1}{-10} = -\frac{1}{10} \]
Now, evaluate \(\left( \frac{h}{g} \right)(-6)\):
\[ \left( \frac{h}{g} \right)(-6) = \frac{h(-6)}{g(-6)} = \frac{-\frac{1}{10}}{12} = \frac{-1}{10 \times 12} = \frac{-1}{120} \]
Therefore, \(\left( \frac{h}{g} \right)(-6)\) is:
\[ \boxed{-\frac{1}{120}} \]
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