Given the relations A: (3,2), (5,3), (6,2), (7,4) which statement is true?

Both A and A^-1 are functions

Neither A nor A^-1 is a function

Only A is a function

Only A^-1 is a function

Option 3.

Step-by-step explanation:

The given relation is

A = { (3,2), (5,3), (6,2), (7,4) }

A relation is called a function, if there exist a unique value of y for each value of x.

In relation A, there exist unique output for each input. So, A is a function.

If a relation is defined as R = { (a, b), a∈R, b∈R}, then inverse of R is

R⁻¹ = { (b, a), a∈R, b∈R}

So, inverse of A is defined as

A⁻¹ = { (2,3), (3,5), (2,6), (4,7) }

Here, the value of y are 3 and 6 at x=2.

For x=2, there exist more than one output. So, A⁻¹ is not a function.

Therefore, the correct option is 3.