Question

Consider the set of values of the independent variable $x$ and dependent variable $y.$

$x=\{3,5,7,11\}$
$y=\{121,25,9\}$

Is this a function? If not, what changes must be done to convert the given relation to a function?

• A. Yes, it is a function.
• B. $49$ must be included in the domain or $7$ must be exluded form the range.
• C. $7$ must be excluded from the domain or $49$ must be included in the range.
• D. None of the above.

Answer 1

Answer: (B), (C)

$7$ must be excluded from the domain or $49$ must be included in the range.

Here the domain is the values of $x.$
$3,5,7,11$ are the prime numbers between $3$ and $11.$

The range is the values of $y.$
$y$ is the square of the correspoinding values of $x.$
$\to 3^2=9$
$\to 5^2=25$
$\to {11}^2=121$

However, $7$ does not have any corresponding value in the range.
$\therefore 7^2=49$ must be included in the range to make the relation a function.

Also, $7$ can be excluded from the domain, such that no element in the domain remains unmapped.

In such case, the defination of domain would be all the prime number between $3$ and $11$ except $7.$
$\to$ Domain: $\{3,5,11\}$
$\to$ Range: $\{121,25,9\}$