IIT JAM Exam > IIT JAM Questions > Let f, g : [0, 1] [0, 1] be functions. Let R(...
Start Learning for Free
Let f, g : [0, 1] → [0, 1] be functions. Let R(f) and R(g) be the ranges of f and g, respectively.
Which of the following statements is (are) true?
Which of the following statements is (are) true?
- a)If f(x) ≤ g(x) for all x ∈ [0, 1], then sup R(f) ≤ inf R(g)
- b)If f(x) ≤ g(x) for some x ∈ [0, 1], then inf R(f) ≤ sup R(g)
- c)If f(x) ≤ g(x) for some x,y ∈ [0, 1], then inf R(f) ≤ sup R(g)
- d)If f(x) ≤ g(x) for all x,y ∈, then sup R(f) ≤ inf R(g)
Correct answer is option 'B,C,D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Let f, g : [0, 1] [0, 1] be functions. Let R(f) and R(g) be the ranges...
Solution:
Definitions:
Explanation:
Therefore, the correct statements are B, C, and D.
Definitions:
- R(f) is the range of function f
- sup R(f) is the supremum of the range of function f
- inf R(g) is the infimum of the range of function g
- f(x) g(x) means that function f is less than or equal to function g for all x in the domain [0,1]
Explanation:
- If f(x) ≤ g(x) for all x [0, 1]:
- sup R(f) ≤ sup R(g) because the supremum of f's range is less than or equal to the supremum of g's range
- inf R(f) ≤ inf R(g) is not necessarily true since it is possible for f to have a smaller range than g even though f is less than or equal to g
- If f(x) ≤ g(x) for some x in [0, 1]:
- inf R(f) ≤ inf R(g) because the infimum of f's range is less than or equal to the infimum of g's range
- sup R(f) ≤ sup R(g) is not necessarily true since it is possible for g to have a larger range than f even though f is less than or equal to g for some x in [0, 1]
- If f(x) ≤ g(x) for some x and y in [0, 1]:
- inf R(f) ≤ inf R(g) because the infimum of f's range is less than or equal to the infimum of g's range
- sup R(f) ≤ sup R(g) because the supremum of f's range is less than or equal to the supremum of g's range
- If f(x) ≤ g(x) for all x and y in [0, 1]:
- inf R(f) ≤ inf R(g) because the infimum of f's range is less than or equal to the infimum of g's range
- sup R(f) ≤ sup R(g) because the supremum of f's range is less than or equal to the supremum of g's range
Therefore, the correct statements are B, C, and D.
|
Explore Courses for IIT JAM exam
|
|
Similar IIT JAM Doubts
Let f, g : [0, 1] [0, 1] be functions. Let R(f) and R(g) be the ranges of f and g, respectively.Which of the following statements is (are) true?a)If f(x) g(x) for all x [0, 1], then sup R(f) inf R(g)b)If f(x) g(x)for some x [0, 1], then inf R(f) sup R(g)c)If f(x) g(x) for some x,y [0, 1], then inf R(f)sup R(g)d)If f(x) g(x)for all x,y, then sup R(f) inf R(g)Correct answer is option 'B,C,D'. Can you explain this answer?
Question Description
Let f, g : [0, 1] [0, 1] be functions. Let R(f) and R(g) be the ranges of f and g, respectively.Which of the following statements is (are) true?a)If f(x) g(x) for all x [0, 1], then sup R(f) inf R(g)b)If f(x) g(x)for some x [0, 1], then inf R(f) sup R(g)c)If f(x) g(x) for some x,y [0, 1], then inf R(f)sup R(g)d)If f(x) g(x)for all x,y, then sup R(f) inf R(g)Correct answer is option 'B,C,D'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Let f, g : [0, 1] [0, 1] be functions. Let R(f) and R(g) be the ranges of f and g, respectively.Which of the following statements is (are) true?a)If f(x) g(x) for all x [0, 1], then sup R(f) inf R(g)b)If f(x) g(x)for some x [0, 1], then inf R(f) sup R(g)c)If f(x) g(x) for some x,y [0, 1], then inf R(f)sup R(g)d)If f(x) g(x)for all x,y, then sup R(f) inf R(g)Correct answer is option 'B,C,D'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f, g : [0, 1] [0, 1] be functions. Let R(f) and R(g) be the ranges of f and g, respectively.Which of the following statements is (are) true?a)If f(x) g(x) for all x [0, 1], then sup R(f) inf R(g)b)If f(x) g(x)for some x [0, 1], then inf R(f) sup R(g)c)If f(x) g(x) for some x,y [0, 1], then inf R(f)sup R(g)d)If f(x) g(x)for all x,y, then sup R(f) inf R(g)Correct answer is option 'B,C,D'. Can you explain this answer?.
Let f, g : [0, 1] [0, 1] be functions. Let R(f) and R(g) be the ranges of f and g, respectively.Which of the following statements is (are) true?a)If f(x) g(x) for all x [0, 1], then sup R(f) inf R(g)b)If f(x) g(x)for some x [0, 1], then inf R(f) sup R(g)c)If f(x) g(x) for some x,y [0, 1], then inf R(f)sup R(g)d)If f(x) g(x)for all x,y, then sup R(f) inf R(g)Correct answer is option 'B,C,D'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Let f, g : [0, 1] [0, 1] be functions. Let R(f) and R(g) be the ranges of f and g, respectively.Which of the following statements is (are) true?a)If f(x) g(x) for all x [0, 1], then sup R(f) inf R(g)b)If f(x) g(x)for some x [0, 1], then inf R(f) sup R(g)c)If f(x) g(x) for some x,y [0, 1], then inf R(f)sup R(g)d)If f(x) g(x)for all x,y, then sup R(f) inf R(g)Correct answer is option 'B,C,D'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f, g : [0, 1] [0, 1] be functions. Let R(f) and R(g) be the ranges of f and g, respectively.Which of the following statements is (are) true?a)If f(x) g(x) for all x [0, 1], then sup R(f) inf R(g)b)If f(x) g(x)for some x [0, 1], then inf R(f) sup R(g)c)If f(x) g(x) for some x,y [0, 1], then inf R(f)sup R(g)d)If f(x) g(x)for all x,y, then sup R(f) inf R(g)Correct answer is option 'B,C,D'. Can you explain this answer?.
Solutions for Let f, g : [0, 1] [0, 1] be functions. Let R(f) and R(g) be the ranges of f and g, respectively.Which of the following statements is (are) true?a)If f(x) g(x) for all x [0, 1], then sup R(f) inf R(g)b)If f(x) g(x)for some x [0, 1], then inf R(f) sup R(g)c)If f(x) g(x) for some x,y [0, 1], then inf R(f)sup R(g)d)If f(x) g(x)for all x,y, then sup R(f) inf R(g)Correct answer is option 'B,C,D'. Can you explain this answer? in English & in Hindi are available as part of our courses for IIT JAM.
Download more important topics, notes, lectures and mock test series for IIT JAM Exam by signing up for free.
Here you can find the meaning of Let f, g : [0, 1] [0, 1] be functions. Let R(f) and R(g) be the ranges of f and g, respectively.Which of the following statements is (are) true?a)If f(x) g(x) for all x [0, 1], then sup R(f) inf R(g)b)If f(x) g(x)for some x [0, 1], then inf R(f) sup R(g)c)If f(x) g(x) for some x,y [0, 1], then inf R(f)sup R(g)d)If f(x) g(x)for all x,y, then sup R(f) inf R(g)Correct answer is option 'B,C,D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let f, g : [0, 1] [0, 1] be functions. Let R(f) and R(g) be the ranges of f and g, respectively.Which of the following statements is (are) true?a)If f(x) g(x) for all x [0, 1], then sup R(f) inf R(g)b)If f(x) g(x)for some x [0, 1], then inf R(f) sup R(g)c)If f(x) g(x) for some x,y [0, 1], then inf R(f)sup R(g)d)If f(x) g(x)for all x,y, then sup R(f) inf R(g)Correct answer is option 'B,C,D'. Can you explain this answer?, a detailed solution for Let f, g : [0, 1] [0, 1] be functions. Let R(f) and R(g) be the ranges of f and g, respectively.Which of the following statements is (are) true?a)If f(x) g(x) for all x [0, 1], then sup R(f) inf R(g)b)If f(x) g(x)for some x [0, 1], then inf R(f) sup R(g)c)If f(x) g(x) for some x,y [0, 1], then inf R(f)sup R(g)d)If f(x) g(x)for all x,y, then sup R(f) inf R(g)Correct answer is option 'B,C,D'. Can you explain this answer? has been provided alongside types of Let f, g : [0, 1] [0, 1] be functions. Let R(f) and R(g) be the ranges of f and g, respectively.Which of the following statements is (are) true?a)If f(x) g(x) for all x [0, 1], then sup R(f) inf R(g)b)If f(x) g(x)for some x [0, 1], then inf R(f) sup R(g)c)If f(x) g(x) for some x,y [0, 1], then inf R(f)sup R(g)d)If f(x) g(x)for all x,y, then sup R(f) inf R(g)Correct answer is option 'B,C,D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let f, g : [0, 1] [0, 1] be functions. Let R(f) and R(g) be the ranges of f and g, respectively.Which of the following statements is (are) true?a)If f(x) g(x) for all x [0, 1], then sup R(f) inf R(g)b)If f(x) g(x)for some x [0, 1], then inf R(f) sup R(g)c)If f(x) g(x) for some x,y [0, 1], then inf R(f)sup R(g)d)If f(x) g(x)for all x,y, then sup R(f) inf R(g)Correct answer is option 'B,C,D'. Can you explain this answer? tests, examples and also practice IIT JAM tests.
|
|
Explore Courses for IIT JAM exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup