Algebra Examples

$f = ((1, 2), (3, 4))$ , $g = ((5, 6), (7, 8))$

Step 1

Since there is one value of $y$ for every value of $x$ in $(1, 2), (3, 4)$ , 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: ${1, 3}$

Range: ${2, 4}$

Step 3

Since there is one value of $y$ for every value of $x$ in $(5, 6), (7, 8)$ , 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: ${5, 7}$

Range: ${6, 8}$

Step 5

The domain of the first relation $f = ((1, 2), (3, 4))$ is not equal to the range of the second relation $g = ((5, 6), (7, 8))$ and the range of the first relation is not equal to the domain of the second relation $g = ((5, 6), (7, 8))$ , which means that $f = ((1, 2), (3, 4))$ is not the inverse of $g = ((5, 6), (7, 8))$ and vice versa.

$f = ((1, 2), (3, 4))$ is not the inverse of $g = ((5, 6), (7, 8))$

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