+0

# algebra

+1
25
1
+67

If  is a function f(x)whose domain is[-8,8] , and g(x)=f(x/2) , then the domain of g(x) is an interval of what width?

Nov 23, 2023
edited by USERSPPB  Nov 23, 2023

#1
+67
+2

Since we defined  g(x)=f(x/2), a real number x is in the domain of g if and only if x/2  is in the domain of f . Therefore, the domain of g consists of all x such that

-8<=x<=8

The solutions to this inequality are given by -16<=x<=16.

so , the domain of g is interval of width 16-(-16)=32.

Nov 23, 2023
The text contains a mathematical question about the domain of a transformed function, and it provides a detailed answer to that question.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
+0

# algebra

+1
25
1
+67

If  is a function f(x)whose domain is[-8,8] , and g(x)=f(x/2) , then the domain of g(x) is an interval of what width?

Nov 23, 2023
edited by USERSPPB  Nov 23, 2023

#1
+67
+2

Since we defined  g(x)=f(x/2), a real number x is in the domain of g if and only if x/2  is in the domain of f . Therefore, the domain of g consists of all x such that

-8<=x<=8

The solutions to this inequality are given by -16<=x<=16.

so , the domain of g is interval of width 16-(-16)=32.

Nov 23, 2023
user
The text contains a mathematical question about the domain of a transformed function, and it provides a detailed answer to that question.

TYPE: SINGLE_QUESTION_WITH_ANSWER