Examples

f = ((0, 7), (9, 6), (4, 3))

$f = ((0, 7), (9, 6), (4, 3))$ ,

g = ((7, 0), (6, 9), (3, 4))

$g = ((7, 0), (6, 9), (3, 4))$

Step 1

Since there is one value of

y

$y$ for every value of

x

$x$ in

(0, 7), (9, 6), (4, 3)

$(0, 7), (9, 6), (4, 3)$ , this relation is a function.

The relation is a function.

Step 2

The domain is the set of all the values of

x

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

y

$y$ .

Domain:

{0, 9, 4}

${0, 9, 4}$

Range:

{7, 6, 3}

${7, 6, 3}$

Step 3

Since there is one value of

y

$y$ for every value of

x

$x$ in

(7, 0), (6, 9), (3, 4)

$(7, 0), (6, 9), (3, 4)$ , 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:

{7, 6, 3}

${7, 6, 3}$

Range:

{0, 9, 4}

${0, 9, 4}$

Step 5

The domain of the first relation

f = ((0, 7), (9, 6), (4, 3))

$f = ((0, 7), (9, 6), (4, 3))$ is equal to the range of the second relation

g = ((7, 0), (6, 9), (3, 4))

$g = ((7, 0), (6, 9), (3, 4))$ . Also, the range of the first relation is equal to the domain of the second relation

g = ((7, 0), (6, 9), (3, 4))

$g = ((7, 0), (6, 9), (3, 4))$ , which means that

f = ((0, 7), (9, 6), (4, 3))

$f = ((0, 7), (9, 6), (4, 3))$ is the inverse of

g = ((7, 0), (6, 9), (3, 4))

$g = ((7, 0), (6, 9), (3, 4))$ and vice versa.

f = ((0, 7), (9, 6), (4, 3))

$f = ((0, 7), (9, 6), (4, 3))$ is the inverse of

g = ((7, 0), (6, 9), (3, 4))

$g = ((7, 0), (6, 9), (3, 4))$

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