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If the function f: R → R defined by
  • a)
    can be made discontinuous on any rational point in the interval [0, 1] by a proper choice of n
  • b)
    can not be made discontinuous on any rational points in the interval [0.1] by a proper choice of n
  • c)
    is continuous everywhere on R
  • d)
    is discontinuous everywhere on R
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If the function f: R → R defined bya)can be made discontinuous on...
Let x be rational say p/q. where p and q are integers prime to each other. Then taken n = q, we see that

is an integral multiple of π and therefore sin n ! πx = 0
but cos n ! πx = 1 or -1 according as n ! x is an even or an odd integer. Now

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Most Upvoted Answer
If the function f: R → R defined bya)can be made discontinuous on...
Let x be rational say p/q. where p and q are integers prime to each other. Then taken n = q, we see that

is an integral multiple of π and therefore sin n ! πx = 0
but cos n ! πx = 1 or -1 according as n ! x is an even or an odd integer. Now

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If the function f: R → R defined bya)can be made discontinuous on any rational point in the interval [0, 1] by a proper choice of nb)can not be made discontinuous on any rational points in the interval [0.1] by a proper choice of nc)is continuous everywhere on Rd)is discontinuous everywhere on RCorrect answer is option 'A'. Can you explain this answer?
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If the function f: R → R defined bya)can be made discontinuous on any rational point in the interval [0, 1] by a proper choice of nb)can not be made discontinuous on any rational points in the interval [0.1] by a proper choice of nc)is continuous everywhere on Rd)is discontinuous everywhere on RCorrect answer is option 'A'. 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 If the function f: R → R defined bya)can be made discontinuous on any rational point in the interval [0, 1] by a proper choice of nb)can not be made discontinuous on any rational points in the interval [0.1] by a proper choice of nc)is continuous everywhere on Rd)is discontinuous everywhere on RCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the function f: R → R defined bya)can be made discontinuous on any rational point in the interval [0, 1] by a proper choice of nb)can not be made discontinuous on any rational points in the interval [0.1] by a proper choice of nc)is continuous everywhere on Rd)is discontinuous everywhere on RCorrect answer is option 'A'. Can you explain this answer?.
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