Which function has an inverse that is also a function?
{(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)}
{(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)}
{(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}
{(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}

A set of ordered pairs, like the ones shown, represents a function only if each of the first coordinates is not repeated.

For example {(2, 5), (7, 8)} is a function, but {(2, 3), (6, 8), (2, -1)} is not because 2 is repeated.

We can check that each set of pairs we are given, are functions.

The inverses of each of these sets would be :

{(–2, –1), (4, 0), (3, 1), (14, 5), (4, 7)}         4 repeats

{(2, -1), (4, 0), (5, 1), (4, 5), (2, 7)}             4 and 2 repeat

{(3, -1), (4, 0), (14, 1), (6, 5), (2, 7)}          no repetition of 1st coordinates

{(4, -1), (4, 0), (2, 1), (3, 5), (1, 7)}             4 repeats


So only the inverse of {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} is also a function