Examples

$f = ((2, 3), (4, 5), (7, 6))$ , $h = ((3, 2), (5, 4), (5, 7))$

Step 1

Since there is one value of $y$ for every value of $x$ in $(2, 3), (4, 5), (7, 6)$ , this relation is a function.

The relation is a function.

Step 2

The domain is the set of all the values of $x$ . The range is the set of all the values of $y$ .

Domain: ${2, 4, 7}$

Range: ${3, 5, 6}$

Step 3

Since $x = 5$ produces $y = 4$ and $y = 7$ , the relation $(3, 2), (5, 4), (5, 7)$ is not a function.

The relation is not a function.

Step 4

The relation $h = ((3, 2), (5, 4), (5, 7))$ is not a function, so there is no inverse for such relation.

$f = ((2, 3), (4, 5), (7, 6))$ is not the inverse of $h = ((3, 2), (5, 4), (5, 7))$

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