Algebra Examples

f = ((8, 9), (7, 1), (4, 3))

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

g = ((9, 8), (1, 7), (3, 4))

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

Step 1

Since there is one value of

y

$y$ for every value of

x

$x$ in

(8, 9), (7, 1), (4, 3)

$(8, 9), (7, 1), (4, 3)$ , this relation is a function.

The relation is a function.

Step 2

The domain is the set of all the values of

x

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

y

$y$ .

Domain:

{8, 7, 4}

${8, 7, 4}$

Range:

{9, 1, 3}

${9, 1, 3}$

Step 3

Since there is one value of

y

$y$ for every value of

x

$x$ in

(9, 8), (1, 7), (3, 4)

$(9, 8), (1, 7), (3, 4)$ , 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:

{9, 1, 3}

${9, 1, 3}$

Range:

{8, 7, 4}

${8, 7, 4}$

Step 5

The domain of the first relation

f = ((8, 9), (7, 1), (4, 3))

$f = ((8, 9), (7, 1), (4, 3))$ is equal to the range of the second relation

g = ((9, 8), (1, 7), (3, 4))

$g = ((9, 8), (1, 7), (3, 4))$ . Also, the range of the first relation is equal to the domain of the second relation

g = ((9, 8), (1, 7), (3, 4))

$g = ((9, 8), (1, 7), (3, 4))$ , which means that

f = ((8, 9), (7, 1), (4, 3))

$f = ((8, 9), (7, 1), (4, 3))$ is the inverse of

g = ((9, 8), (1, 7), (3, 4))

$g = ((9, 8), (1, 7), (3, 4))$ and vice versa.

f = ((8, 9), (7, 1), (4, 3))

$f = ((8, 9), (7, 1), (4, 3))$ is the inverse of

g = ((9, 8), (1, 7), (3, 4))

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

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