How Do We Calculate (f O g) for Given Functions and Set A?

[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
$$h(x) = f(g(x))$$