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 + g

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:

$f + g$

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 1 and 3, because for points 2 and 4 we have no value for $g$, for point 5 we have no value for $f$. The domain of the function is a set of all values for which it is exist. That's why:

$$f + g (1) = 2 + (-2) = 0; f + g (3) = 4 + (-3) = 1.$$