# HOW TO FIND FOG AND GOF FROM THE GIVEN RELATIONS F AND G

Problem 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 defined. Also find fog and gof.

Solution

Problem 2 :

Let f = { (1, -1) (4, -2) (9, -3) (16, 4) }

and

g = { (-1, -2) (-2, -4) (-3, -6) (4, 8) }

Show that gof is defined while fog is not defined. Also find gof.

Solution

Problem 3 :

If

f = {(1,3) (2,1) (3,4) (4,2)}

and

g = {(1,2) (2,3) (3,4) (4,1)}

then find n(fog)

Solution

Problem 4 :

If

f = {(1, 4), (2, 5), (3, 6)} and g = {(4, 8), (5, 7), (6, 9)}

then gof is

a) { }                  b) {(1,8), (2, 7), (3, 9)}

c) {(1,7), (2, 8), (3, 9)}             d) {(1,8), (2, 5), (3, 9)}

Solution

1)  fog = { (1, 1), (3, 1), (4, 3), (5, 3) }

gof = { (3, 3) (9, 3) (12, 9) }

2)  gof = { (1, -2) (4, -4) (9, -6) (16, 8) }

There is no input -2 in the relation f. So, the function fog is not defined.

3)  n[fog] = 4

4)  fog = { (1, 8), (2, 7) (3, 9) }, option b

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