Examples

$f = ((8, 9), (0, 1), (4, 3))$ , $g = ((9, 8), (1, 7), (3, 3))$

Step 1

Since there is one value of $y$ for every value of $x$ in $(8, 9), (0, 1), (4, 3)$ , 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: ${8, 0, 4}$

Range: ${9, 1, 3}$

Step 3

Since there is one value of $y$ for every value of $x$ in $(9, 8), (1, 7), (3, 3)$ , this relation is a function.

The relation is a function.

Step 4

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

Domain: ${9, 1, 3}$

Range: ${8, 7, 3}$

Step 5

The range of the first relation $f = ((8, 9), (0, 1), (4, 3))$ is equal to the domain of the second relation $g = ((9, 8), (1, 7), (3, 3))$ . However, The domain of the first relation $f = ((8, 9), (0, 1), (4, 3))$ is not equal to the range of the second relation $g = ((9, 8), (1, 7), (3, 3))$ , which means that $f = ((8, 9), (0, 1), (4, 3))$ is not the inverse of $g = ((9, 8), (1, 7), (3, 3))$ and vice versa.

$f = ((8, 9), (0, 1), (4, 3))$ is not the inverse of $g = ((9, 8), (1, 7), (3, 3))$

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