Let f = {(3, 1), (9, 3), (12, 4)} and g = {(1, 3), (3, 3), (4, 9), (5,

1.	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.
Answer» 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)}

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.

Answer»

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)}