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If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?
- a)–4
- b)–5
- c)–6
- d)–7
- e)–9
Correct answer is option 'E'. Can you explain this answer?
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Most Upvoted Answer
If the function f(x) is defined for all real numbers x as the maximum ...
Understanding the Function f(x)
The function \( f(x) \) is defined as the maximum of two linear functions:
- \( 2x + 4 \)
- \( 12 + 3x \)
To find when \( f(x) = 2x + 4 \), we must determine where \( 2x + 4 \) is greater than or equal to \( 12 + 3x \).
Finding the Intersection Point
1. Set the two functions equal to each other:
\[
2x + 4 = 12 + 3x
\]
2. Rearranging the equation gives:
\[
2x - 3x = 12 - 4
\]
\[
-x = 8 \quad \Rightarrow \quad x = -8
\]
Analyzing the Regions
- To the left of \( x = -8 \) (i.e., \( x < -8="" \)),="" \(="" 2x="" +="" 4="" \)="" will="" be="" greater="" than="" \(="" 12="" +="" 3x="" />
- To the right of \( x = -8 \) (i.e., \( x > -8 \)), \( 12 + 3x \) will be greater than \( 2x + 4 \).
Thus, for values of \( x < -8="" \),="" \(="" f(x)="2x" +="" 4="" />
Evaluating Given Options
Now, we check the provided options to find the largest value less than \(-8\):
- a) \(-4\) (not valid)
- b) \(-5\) (not valid)
- c) \(-6\) (not valid)
- d) \(-7\) (not valid)
- e) \(-9\) (valid)
Conclusion
The only value among the options where \( f(x) = 2x + 4 \) is when \( x = -9 \). Thus, the correct answer is option E: \(-9\).
The function \( f(x) \) is defined as the maximum of two linear functions:
- \( 2x + 4 \)
- \( 12 + 3x \)
To find when \( f(x) = 2x + 4 \), we must determine where \( 2x + 4 \) is greater than or equal to \( 12 + 3x \).
Finding the Intersection Point
1. Set the two functions equal to each other:
\[
2x + 4 = 12 + 3x
\]
2. Rearranging the equation gives:
\[
2x - 3x = 12 - 4
\]
\[
-x = 8 \quad \Rightarrow \quad x = -8
\]
Analyzing the Regions
- To the left of \( x = -8 \) (i.e., \( x < -8="" \)),="" \(="" 2x="" +="" 4="" \)="" will="" be="" greater="" than="" \(="" 12="" +="" 3x="" />
- To the right of \( x = -8 \) (i.e., \( x > -8 \)), \( 12 + 3x \) will be greater than \( 2x + 4 \).
Thus, for values of \( x < -8="" \),="" \(="" f(x)="2x" +="" 4="" />
Evaluating Given Options
Now, we check the provided options to find the largest value less than \(-8\):
- a) \(-4\) (not valid)
- b) \(-5\) (not valid)
- c) \(-6\) (not valid)
- d) \(-7\) (not valid)
- e) \(-9\) (valid)
Conclusion
The only value among the options where \( f(x) = 2x + 4 \) is when \( x = -9 \). Thus, the correct answer is option E: \(-9\).
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If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?a)–4b)–5c)–6d)–7e)–9Correct answer is option 'E'. Can you explain this answer?
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If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?a)–4b)–5c)–6d)–7e)–9Correct answer is option 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?a)–4b)–5c)–6d)–7e)–9Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?a)–4b)–5c)–6d)–7e)–9Correct answer is option 'E'. Can you explain this answer?.
If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?a)–4b)–5c)–6d)–7e)–9Correct answer is option 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?a)–4b)–5c)–6d)–7e)–9Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?a)–4b)–5c)–6d)–7e)–9Correct answer is option 'E'. Can you explain this answer?.
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