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Relations and Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsRelations and Functions1 Mark
MCQ
Which one of the following is not a function?
  • A
    $\{(\text{x, y}):\text{x},\text{ y}\in\text{R},\text{x}^2=\text{y}\}$
  • ✓
    $\{(\text{x, y}):\text{x},\text{ y}\in\text{R},\text{y}^2=\text{x}\}$
  • C
    $\{(\text{x, y}):\text{x},\text{ y}\in\text{R},\text{x}^2=\text{y}^3\}$
  • D
    $\{(\text{x, y}):\text{x},\text{y}\in\text{R},\text{y}=\text{x}^3\}$
✓

Answer

Correct option: B.
$\{(\text{x, y}):\text{x},\text{ y}\in\text{R},\text{y}^2=\text{x}\}$
$y^2 = x$ gives two values of $y$ for a value of $x$
i.e. there are two images for a value of $x.$
For example: $(2)^2 = 4$ and $(-2)^2 = 4$
Thus, it is not a function.

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