Question

Determine the domain and range of the relation R Defined by R=(x, x+5) : $x\in \\{ 1,\ 2,\ 3,\ 4,\ 5\\}$.

Answer 1

Hint: In this question it is given given that we have to find the domain and range of the relation R where R=(x, x+5), such that $x\in \\{ 1,\ 2,\ 3,\ 4,\ 5\\}$.
So to find the domain we have to take the set of all the possible values of x and the range will be the set of all second elements of ordered pairs (y-coordinates).

Complete step-by-step answer:
Here it is given that x belongs to {1, 2, 3, 4, 5} , that means the possible values of x is {1, 2, 3, 4, 5}.
Which implies the domain set is {1, 2, 3, 4, 5}
Now we have to find the y-coordinates for each value of x,
Here it is given, y=x+5
So, when x=1, y=1+5=6
If x=2, then y=2+5=7
If x=3 then y=3+5=8
If x=4 then y=4+5=9
And lastly when x=5, y=5+5=10
Therefore the possible values of y is {6, 7, 8, 9, 10}
Which is called the range of the relation R.
Hence the domain set is {1, 2, 3, 4, 5} and the range set {6, 7, 8, 9, 10}.

Note: While solving this type of question you need to know that all of the values that can go into a relation or function (input) are called the domain and the values that come out of a relation or function (output) are called the range.
Also you can identify the domain and range from the relation set, which is the collection of all possible ordered pairs.The domain is the set of all first elements of ordered pairs (x-coordinates) and the range is the set of all second elements of ordered pairs (y-coordinates).