Precalculus Examples

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

Step 1

Since there is one value of $y$ for every value of $x$ in $(0, 7), (9, 6), (4, 3)$ , this relation is a function.

The relation is a function.

Step 2

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

Domain: ${0, 9, 4}$

Range: ${7, 6, 3}$

Step 3

Since there is one value of $y$ for every value of $x$ in $(7, 0), (6, 9), (3, 4)$ , this relation is a function.

The relation is a function.

Step 4

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

Domain: ${7, 6, 3}$

Range: ${0, 9, 4}$

Step 5

The domain of the first relation $f = ((0, 7), (9, 6), (4, 3))$ is equal to the range of the second relation $g = ((7, 0), (6, 9), (3, 4))$ . Also, the range of the first relation is equal to the domain of the second relation $g = ((7, 0), (6, 9), (3, 4))$ , which means that $f = ((0, 7), (9, 6), (4, 3))$ is the inverse of $g = ((7, 0), (6, 9), (3, 4))$ and vice versa.

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

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