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The function f (x) = | x | has
- a)only one minima
- b)no maxima or minima
- c)only one maxima
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The functionf(x)= |x|hasa)only one minimab)no maxima or minimac)only o...
The modulus function has V-shaped graph,which means that it has only one minima.
Most Upvoted Answer
The functionf(x)= |x|hasa)only one minimab)no maxima or minimac)only o...
Understanding the Function f(x) = |x|
The function f(x) = |x| is a well-known absolute value function. Let’s analyze its characteristics to understand why the correct answer is option 'A', which states that it has only one minimum.
Graph of the Function
- The graph of f(x) = |x| is a V-shaped curve that opens upwards.
- The vertex of the graph is at the point (0, 0), which is the lowest point on the graph.
Minimum Point
- The function achieves its minimum value at x = 0.
- At this point, f(0) = |0| = 0, which is the lowest value that the function can take.
- Since the function approaches infinity as x moves away from 0 in both positive and negative directions, it confirms that there is only one minimum.
Maxima and Other Characteristics
- The function does not have any maximum points. As x approaches positive or negative infinity, f(x) continues to increase.
- There are no other turning points in the graph; it is monotonically increasing on both sides of the minimum.
Conclusion
- Therefore, the function f(x) = |x| has only one minimum at (0, 0) and no maxima.
- This leads us to conclude that the correct answer is indeed option 'A', confirming the function’s unique minimum characteristics and absence of maxima or additional minima.
The function f(x) = |x| is a well-known absolute value function. Let’s analyze its characteristics to understand why the correct answer is option 'A', which states that it has only one minimum.
Graph of the Function
- The graph of f(x) = |x| is a V-shaped curve that opens upwards.
- The vertex of the graph is at the point (0, 0), which is the lowest point on the graph.
Minimum Point
- The function achieves its minimum value at x = 0.
- At this point, f(0) = |0| = 0, which is the lowest value that the function can take.
- Since the function approaches infinity as x moves away from 0 in both positive and negative directions, it confirms that there is only one minimum.
Maxima and Other Characteristics
- The function does not have any maximum points. As x approaches positive or negative infinity, f(x) continues to increase.
- There are no other turning points in the graph; it is monotonically increasing on both sides of the minimum.
Conclusion
- Therefore, the function f(x) = |x| has only one minimum at (0, 0) and no maxima.
- This leads us to conclude that the correct answer is indeed option 'A', confirming the function’s unique minimum characteristics and absence of maxima or additional minima.
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The functionf(x)= |x|hasa)only one minimab)no maxima or minimac)only one maximad)none of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The functionf(x)= |x|hasa)only one minimab)no maxima or minimac)only one maximad)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The functionf(x)= |x|hasa)only one minimab)no maxima or minimac)only one maximad)none of theseCorrect answer is option 'A'. Can you explain this answer?.
The functionf(x)= |x|hasa)only one minimab)no maxima or minimac)only one maximad)none of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The functionf(x)= |x|hasa)only one minimab)no maxima or minimac)only one maximad)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The functionf(x)= |x|hasa)only one minimab)no maxima or minimac)only one maximad)none of theseCorrect answer is option 'A'. Can you explain this answer?.
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