It is known that there is a rational number between any two distinct irrational numbers. Consider a continuous function such that for every rational number . If is an irrational number, then:
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0 marksMathematicsLimits, continuity and differentiabilityContinuity and discontinuitiesModerateabout 2 min
DSE 2019 Question 14: Limits, continuity and differentiability
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It is known that there is a rational number between any two distinct irrational numbers. Consider a continuous function f:ℜ→ℜ such that f(x)=sin x for every rational number x. If x is an irrational number, then: (A) f(x)=sin x (B) f(x)=(sin x)/2+(cos x)/2 (C) f(x)=sin (x/2)+cos (x/2) (D) f(x)=cos x
Also written as: It is known that there is a rational number between any two distinct irrational numbers. Consider a continuous function f: Re -> Re such that f(x)=sin x for every rational number x. If x is an irrational number, then:
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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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