Examples

f = ((1, 2), (3, 4))

$f = ((1, 2), (3, 4))$ ,

g = ((5, 6), (7, 8))

$g = ((5, 6), (7, 8))$

Step 1

Since there is one value of

y

$y$ for every value of

x

$x$ in

(1, 2), (3, 4)

$(1, 2), (3, 4)$ , this relation is a function.

The relation is a function.

Step 2

The domain is the set of all the values of

x

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

y

$y$ .

Domain:

{1, 3}

${1, 3}$

Range:

{2, 4}

${2, 4}$

Step 3

Since there is one value of

y

$y$ for every value of

x

$x$ in

(5, 6), (7, 8)

$(5, 6), (7, 8)$ , this relation is a function.

The relation is a function.

Step 4

The domain is the set of all the values of

x

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

y

$y$ .

Domain:

{5, 7}

${5, 7}$

Range:

{6, 8}

${6, 8}$

Step 5

The domain of the first relation

f = ((1, 2), (3, 4))

$f = ((1, 2), (3, 4))$ is not equal to the range of the second relation

g = ((5, 6), (7, 8))

$g = ((5, 6), (7, 8))$ and the range of the first relation is not equal to the domain of the second relation

g = ((5, 6), (7, 8))

$g = ((5, 6), (7, 8))$ , which means that

f = ((1, 2), (3, 4))

$f = ((1, 2), (3, 4))$ is not the inverse of

g = ((5, 6), (7, 8))

$g = ((5, 6), (7, 8))$ and vice versa.

f = ((1, 2), (3, 4))

$f = ((1, 2), (3, 4))$ is not the inverse of

g = ((5, 6), (7, 8))

$g = ((5, 6), (7, 8))$

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