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Relations and Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRelations and Functions1 Mark
MCQ
$f : R \rightarrow R$ given by $\text{f(x)}=\text{x}+\sqrt{\text{x}^2}$ is:
  • A
    Injective.
  • B
    Surjective.
  • C
    Bijective.
  • ✓
    None of these.
✓

Answer

Correct option: D.
None of these.
$\text{f(x)}=\text{x}+\sqrt{\text{x}^2}=\text{x}\pm\text{x}=0 $ or $2\text{x}$
$\Rightarrow$ Each element of the domain has $2$ images.
$f$ is not a function.

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