# Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Determine its domain

Domain definition

The set of all possible values which qualify as inputs to a function is known as the domain of the function. In other words the entire set of values possible for independent variables.
The domain can be obtained in – the denominator of the fraction is not equal to zero and the digit under the square root bracket is positive. (In case of a function with fraction values).

### Finding the Domain of a function

Adomain is defined as the set of possible values “x” of a function which will give the output value “y”. It is the set of possible values for the independent variables.

Listed below are the steps to determine the domain of the function

• To determine the domain, consider the values of the independent variables
• The set of all real numbers (R) is considered as the domain of a function subject to some restrictions.
• Domain restrictions refer to the values for which the given function cannot be defined.

### Solution

The relation R from A to A is given as:

R = {(xy): 3x – y = 0, where xy ∈ A}

= {(xy): 3x = y, where xy ∈ A}

So,

R = {(1, 3), (2, 6), (3, 9), (4, 12)}

Now,

The domain of R is the set of all first elements of the ordered pairs in the relation.

Hence, Domain of R = {1, 2, 3, 4}

The whole set A is the codomain of the relation R.

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