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Questions › DSE › DSE 2019 › Q29
0 marksMathematics › Sets, relations and functions › One-to-one, onto and invertible functionsModerateabout 2 min

DSE 2019 Question 29: Sets, relations and functions

Functions f,gf,gf,g from ℜ\Reℜ to ℜ\Reℜ are defined by: f(x)=0f(x)=0f(x)=0 if xxx is rational and f(x)=xf(x)=xf(x)=x if xxx is irrational; g(x)=0g(x)=0g(x)=0 if xxx is irrational and g(x)=xg(x)=xg(x)=x if xxx is rational. Then the function (f−g)(x)(f-g)(x)(f−g)(x) is:

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Functions f,g from ℜ to ℜ are defined by: f(x)=0 if x is rational and f(x)=x if x is irrational; g(x)=0 if x is irrational and g(x)=x if x is rational. Then the function (f-g)(x) is: (A) surjective but not injective (B) injective but not surjective (C) bijective (D) neither injective nor surjective

Also written as: Functions f,g from Re to Re are defined by: f(x)=0 if x is rational and f(x)=x if x is irrational; g(x)=0 if x is irrational and g(x)=x if x is rational. Then the function (f-g)(x) is:

Sets, relations and functions has come up 65 times in 6 exams since 2004.

What this question tests

This question is on One-to-one, onto and invertible functions, part of Sets, relations and functions in Mathematics.

Injective, surjective and bijective functions and when an inverse exists.

TestStop has 11 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2022 · Q13Let f:[0,∞)→ℝ be defined by f(x) = (x+1)/(x+2) for all x in the domain. Then f is
Practise Sets, relations and functionsMore on One-to-one, onto and invertible functions

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Question from the DSE 2019 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.