Algebra Examples

(\frac{1}{3}, \frac{4}{7})

$(\frac{1}{3}, \frac{4}{7})$ ,

(1, 0)

$(1, 0)$

Step 1

Since for each value of

x

$x$ there is one and only one value of

y

$y$ , the given relation

(\frac{1}{3}, \frac{4}{7}), (1, 0)

$(\frac{1}{3}, \frac{4}{7}), (1, 0)$ is a function.

The relation is a function.

Step 2

Since the relation is a function and for each value of

y

$y$ there is one and only one value of

x

$x$ , the given relation

(\frac{1}{3}, \frac{4}{7}), (1, 0)

$(\frac{1}{3}, \frac{4}{7}), (1, 0)$ is a one-to-one function.

The relation is a one-to-one function.

Step 3

Every point in the range is the value of

y

$y$ for at least one point

x

$x$ in the domain, so this is a surjective function.

Surjective function

Step 4

Since

(\frac{1}{3}, \frac{4}{7}), (1, 0)

$(\frac{1}{3}, \frac{4}{7}), (1, 0)$ is injective (one to one) and surjective, then it is bijective function.

Bijective function

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