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.?
1 Answer
# 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 = { (-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