Question

If f = (1, 2), (2, 3), (3, 4), (4, 5),
g = (1, -2), (3, -3), (5, -5), and
h = (1, 0), (2, 1), (3, 2),

find the following and state the domain:

f / h

Answer 1

Conditions

If $f = (1, 2), (2, 3), (3, 4), (4, 5)$,

$g = (1, -2), (3, -3), (5, -5)$, and

$h = (1, 0), (2, 1), (3, 2)$,

find the following and state the domain:

$f / h$

Solution

We can find the following only for those values of these functions, for which they exist.

It's obvious, that these are the points 2 and 3, because for point 1 we have no rights to divide, as $h(1)=0$, for point 4 we have no value for $h$. The domain of the function is a set of all values for which it is exist. That's why:

$$\frac{f}{h}(2) = \frac{3}{1} = 3; \frac{f}{h}(3) = \frac{4}{2} = 2. \text{ The domain of } \frac{f}{h} \text{ is 2 and 3}$$