Is the given relation a function? Give reasons for your answer.

f = {(x, x) | x is a real number}

Given: f = {(x, x) | x is a real number}

To find: whether the given relation is a function with proper reason

Explanation: the given relation is f = {(x, x) | x is a real number}

This means the relation f has elements which are real number.

Here it can be seen that element for every x ∈ R there will be unique image.

And a relation is said to be function if every element of one set has one and only one image in other set.

So, f is a function