functions

[aaa59]

if A={1,2,3}

f:A-> A = {(1,2),(2,3),(3,1)}
g:A->A = {(1,2),(2,1),(3,3)}

how would we calculate (f O g)?

[uman]

say h = f o g. To find h(x), simply plug x into g, and then plug the result into f.

For example, g(2) = 1 and f(1) = 2. So h(2) = 2. Hope this helps.

[aaa59]

i think i got it.

so: g(1) = 2 and f(2) = 3. therefore h(1)=3. am i right?

[uman]

Yes.

[CompuChip]

At this stage, you can just consider
h = f \circ g
as just "shorthand" for the function defined by
h(x) = f(g(x))