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STD 12 - 1. relation and function — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 1. relation and function1 Mark
MCQ
If   $f(x) = \left\{ \begin{array}{l}x,\,\,{\rm{when\,\,}}\,x\,\,{\rm{\,is\,}}\,{\rm{\,rational\,\,}}\\0{\rm{,}}\,\,{\rm{when\,\,}}x{\rm{ \,\,is\,\,\, irrational\,}}\end{array} \right.$;

$g(x) = \left\{ \begin{array}{l}0,\,\,\,\,{\rm{when\,\,}}\,x\,{\rm{\,\,is\,\,}}\,{\rm{\,\,rational\,}}\\x,\,\,\,\,{\rm{\,\,when\,\,}}\,x\,{\rm{\,\,is\,\, irrational\,}}\end{array} \right.$   then $(f - g)$ is

  • ✓
    One-one onto
  • B
    One-one not onto
  • C
    Not one-one but onto
  • D
    Not one-one not onto
✓

Answer

Correct option: A.
One-one onto
a
(a) $(f - g)(x) = \left\{ \begin{array}{l}\,\,\,x,\,\,x \in Q\\ - x,\,\,\,x \notin Q\end{array} \right.$

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