How do you add functions with equal domain sets?

[sfeld]

Two functions are said to be equal if they ahve the same domain and, for each value in the domain set, the function values are equal respectively.

F = {(2,3),(3,4),(4,5)
G = {(3,4),(4,5),(2,3)

The domain sets are equal, and f(x) = g(x) for each corresponding value of the domain.


Tow functions f(x) and g(x) may be added together only for equal domain sets.
Symbolically f(x) + g(x) = (f+g)(x)

F = {(2,3),(5,7),(8,1),(-2,3)
G = {(2,5),(6,7),(9,3),(8,6),(-2,3)

(f+g)(x)={(2,8),(8,7),(-2,6)

Notice that the equal domain set is
D = {2,8,-2}

and the sum of the function values are
{8,7,6}

Im just wondering how they figured that out, where the 2,8; 8,7; -2,6 all came from.

 

[courtrigrad]

(f+g)(x)={(2,8),(8,7),(-2,6) is the result of adding the ordinates of the two functions with the same x value (abscissa)

F = {(2,3),(5,7),(8,1),(-2,3)
G = {(2,5),(6,7),(9,3),(8,6),(-2,3)

Look at the 2 functions.

(2,3) and (2,5) have the same x-value. Hence we add the y-values (because they are common)

We get (2,8)

Do this for the other elements in the function sets.

 

[sfeld]

Thanks for your help, I figured it out I think!