Consider the function defined by where is the set of rational numbers. Then, is
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2 marksMathematicsLimits, continuity and differentiabilityContinuity and discontinuitiesHardabout 4 min
DSE 2011 Question 25: Limits, continuity and differentiability
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Consider the function f:ℜ→ℜ defined by f(x)={ x², if x∈ℚ; 0, otherwise } where ℚ is the set of rational numbers. Then, f is (A) discontinuous at every x≠ 0. (B) continuous at all points in ℚ. (C) continuous at multiple points. (D) discontinuous on a countable set of points.
Also written as: Consider the function f: Re -> Re defined by f(x)={ x^2, if x in Q; 0, otherwise } where Q is the set of rational numbers. Then, f is
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What this question tests
This question is on Continuity and discontinuities, part of Limits, continuity and differentiability in Mathematics.
When a function is continuous at a point and what kinds of breaks occur.
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