Let f = {(3, 1), (9, 3), (12, 4)} and g = {(1, 3), (3, 3), (4, 9), (5, 9)}. Show that gof and fog are both defined, Also, find fog and gof.
Let f = {(3,1), (9,3), (12,4)} and
g = {(1,3), (3,3), (4,9), (5,9)}
Now,
range of f = (1, 3, 4}
domain of f = {3, 9, 12}
range of g = {3,9}
domain of g = (1, 3, 4, 5}
since, range of f ⊂ domain of g
∴ gof is well defined.
Again, the range of g ⊆ domain of f
∴ fog in well defined.
Finally, gof = {(3,3), (9 ,3), (12,9)}
fog = {(1,1) , (3,1), (4,3), (5,3)}