Which of the following are functions? - Vidyadip

MCQ

Which of the following are functions?

A
$\{(\text{x, y}):\text{y}^2=\text{x, x, y}\in\text{R}\}$
B
$\{(\text{x, y}):\text{y}=\text{|x|},\text{x, y}\in\text{R}\}$
C
$\{(\text{x, y}):\text{x}^2+\text{y}^2=1,\text{x, y}\in\text{R}\}$
D
$\{(\text{x, y}):\text{x}^2-\text{y}^2=1\text{x, y}\in\text{R}\}$

✓

Answer

$\{(\text{x, y}):\text{y}=\text{|x|},\text{x, y}\in\text{R}\}$

Solution:

For every value of $\text{x}\in\text{R},$ there is a unique value $\text{y} \in\text{R}$

i.e., there is a unique image for all values of $\text{x}\in\text{R},$

Also, values of x occur only once in the ordered pairs.

Thus, it is a function.

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