InterviewSolution
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InterviewSolution
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Let f(x) be given that `f(x)={{:(,x,"if x is rational"),(,1-x,"if x is irrational"):}` The number of points at which f(x) is continuous, isA. `oo`B. 1C. 0D. none of these |
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Answer» Correct Answer - C Let a be any rational number. Then, there exists a sequence `lt a_(n) gt` of irrational points such that lim `a_(n)=a` We have, `therefore underset(n to oo)lim f(a_(n))=1-a` `Rightarrow underset(n to oo)lim f(a_(n))=1-f(a)" "[therefore f(a)=a]` Thus, lim `a_(n)`=a but lim `f(a_(n)) ne f(a)`. So,f is discontinuous at x=a Similarly, f(x) is discontinuous at all iraational poitns. Hence, f(x) is nowhere continuous |
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