FROM THE GIVEN RELATIONS FIND FOG AND GOF WORKSHEET

Answer Key

1)  a) Finding fog :

(f ∘ g) (0) = 1

(f ∘ g) (1) = 0

(f ∘ g) (2) = 3

(f ∘ g) (3) = 2

f ∘ g = {(0, 1), (1, 0), (2, 3), (3, 2)}

b) Finding gof :

(g ∘ f) (0) = 1

(g ∘ f) (1) = 0

(g ∘ f) (2) = 3

(g ∘ f) (3) = 2

g ∘ f = {(0, 1) (1, 0) (2, 3) (3, 2)}

c) Finding fof :

(f ∘ f) (0) = 0

(f ∘ f) (1) = 1

(f ∘ f) (2) = 2

(f ∘ f) (3) = 3

f ∘ f = {(0, 0), (1, 1), (2, 2), (3, 3)}

2)

(f ∘ g) (0) = 0

(f ∘ g) (1) = 1

(f ∘ g) (2) = 2

(f ∘ g) (3) = 3

f ∘ g = {(0, 0), (1, 1), (2, 2), (3, 3)}

3)

a)  f ∘ g :

(f ∘ g) (0) = 2

(f ∘ g) (1) = 0

(f ∘ g) (2) = 1

(f ∘ g) (3) = 3

f ∘ g = {(0, 2), (1, 0), (2, 1), (3, 3)}

b)  g ∘ f :

(g ∘ f) (2) = 7

(g ∘ f) (5) = 2

(g ∘ f) (7) = 5

(g ∘ f) (9) = 9

g ∘ f = {(2, 7), (5, 2), (7, 5), (9, 9)}

4) a)  a = c

b) a = 1/2 and b = -3/2

c)  So, the result in b is true.