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Which of the following statement is true?
  • a)
    f : D → ℝ where D ⊆ ℝ, be a uniformly continuous function, then f is bounded 
  • b)
    The function f : [0,1]→ℝ , defined as f(x) =  is not uniformly continuous over [0, 1]
  • c)
    f ; [-1, 1] →ℝ defined by f(x) =  is not uniformly continuous on [-1, 1]
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Which of the following statement is true?a)f : D→ whereD ⊆ ,...
(a) Let f(x) = x, x∈[0, ∞], then clearly f(x) is uniformly continuous but not bounded.
(b) Note that  here f is continuous over [0, 1], so f(x) is uniformly continuous.
(c) Note that f(x) = 
Clearly f(x) is not continuous at x = 0, so f(x) is not uniformly continuous.
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Which of the following statement is true?a)f : D→ whereD ⊆ , be a uniformly continuous function, then f is boundedb)The function f : [0,1]→, defined as f(x) =is not uniformly continuous over [0, 1]c)f ; [-1, 1]→defined by f(x) =is not uniformly continuous on [-1, 1]d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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Which of the following statement is true?a)f : D→ whereD ⊆ , be a uniformly continuous function, then f is boundedb)The function f : [0,1]→, defined as f(x) =is not uniformly continuous over [0, 1]c)f ; [-1, 1]→defined by f(x) =is not uniformly continuous on [-1, 1]d)None of theseCorrect answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Which of the following statement is true?a)f : D→ whereD ⊆ , be a uniformly continuous function, then f is boundedb)The function f : [0,1]→, defined as f(x) =is not uniformly continuous over [0, 1]c)f ; [-1, 1]→defined by f(x) =is not uniformly continuous on [-1, 1]d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statement is true?a)f : D→ whereD ⊆ , be a uniformly continuous function, then f is boundedb)The function f : [0,1]→, defined as f(x) =is not uniformly continuous over [0, 1]c)f ; [-1, 1]→defined by f(x) =is not uniformly continuous on [-1, 1]d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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