Question

If `f={(-3,4),(-1,5),(-2,6),(2,4),(0,3)} and g={(4,3),(5,7),(3,0),(6,0)}` then find set of ordered pair of gof and fog and represent in arrow diagram.?

Answer 1

`g \ bb(o) \ f = { (-3,3), (-1,7), (-2,0-), (2,3), (0,0) }`

`f \ bb(o) \ g = {(3,3),(6,3)}`

Explanation:

Given the specified ordered pairs, we can write the functions `f` and `g` by the mappings:

# f = { (-3, |-> 4), (-1, |-> 5), (-2, |-> 6), (2, |-> 4), (0, |-> 3) :} \ \ \ #, and # g = { (4, |-> 3), (5, |-> 7), (3, |-> 0), (6, |-> 0) :} #

We can construct:

`g \ bb(o) \ f = g(f)`

# g \ bb(o) \ f = { (gf(-3)), (gf(-1)), (gf(-2)), (gf(2)), (gf(0)) :} = { (g(4)), (g(5)), (g(6)), (g(4)), (g(3)) :} = { (3), (7), (0), (3), (0) :} #

Thus using an ordered pair representation, we have:

`g \ bb(o) \ f = { (-3,3), (-1,7), (-2,0-), (2,3), (0,0) }`

However, We have a restricted domain for

`g \ bb(o) \ f = g(f)`

We get:

# f \ bb(o) \ g = { (fg(4)), (fg(5)), (fg(3)), (fg(6)) :} = { (f(3)), (f(7)), (f(0)), (f(0)) :} = { ("undefined"), ("undefined"), (3), (3) :} #

The domain of `f@g` is that part of the domain of `g` that yields a value in the domain of `f`.