Let A = {1, 2, 3, 4}. Let f : A → A and g : A → A,defined by f = {

1.	Let A = {1, 2, 3, 4}. Let f : A → A and g : A → A,defined by f = {(1, 4), (2, 1), (3,3),(4, 2)} and g = {(1, 3), (2, 1), (3, 2), (4, 4)}.Find (i) gof (ii) fog (iii) fof.
Answer» (i) gof To find: gof Formula used: g o f = g(f(x)) Given: f = {(1, 4), (2, 1), (3, 3), (4, 2)} and g = {(1, 3), (2, 1), (3, 2), (4, 4)} Solution: We have, gof(1) = g(f(1)) = g(4) = 4 gof(2) = g(f(2)) = g(1) = 3 gof(3) = g(f(3)) = g(3) = 2 gof(4) = g(f(4)) = g(2) = 1 g o f = {(1, 4), (2, 3), (3, 2), (4, 1)} (ii) fog To find: fog Formula used: fog = f(g(x)) Given: f = {(1, 4), (2, 1), (3, 3), (4, 2)} and g = {(1, 3), (2, 1), (3, 2), (4, 4)} Solution: We have, fog(1) = f(g(1)) = f(3) = 3 fog(2) = f(g(2)) = f(1) = 4 fog(3) = f(g(3)) = f(2) = 1 fog(4) = f(g(4)) = f(4) = 2 f o g = {(1, 3), (2, 4), (3, 1), (4, 2)} (iii) fof To find: fof Formula used: f o f = f(f(x)) Given: f = {(1, 4), (2, 1), (3, 3), (4, 2)} Solution: We have, fof(1) = f(f(1)) = f(4) = 2 fof(2) = f(f(2)) = f(1) = 4 fof(3) = f(f(3)) = f(3) = 3 fof(4) = f(f(4)) = f(2) = 1 fof = {(1, 2), (2, 4), (3, 3), (4, 1)}

Let A = {1, 2, 3, 4}. Let f : A → A and g : A → A,defined by f = {(1, 4), (2, 1), (3,3),(4, 2)} and g = {(1, 3), (2, 1), (3, 2), (4, 4)}.Find (i) gof (ii) fog (iii) fof.

Answer»

(i) gof

To find: gof

Formula used: g o f = g(f(x))

Given: f = {(1, 4), (2, 1), (3, 3), (4, 2)} and g = {(1, 3), (2, 1), (3, 2), (4, 4)}

Solution: We have,

gof(1) = g(f(1)) = g(4) = 4

gof(2) = g(f(2)) = g(1) = 3

gof(3) = g(f(3)) = g(3) = 2

gof(4) = g(f(4)) = g(2) = 1

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

(ii) fog

To find: fog

Formula used: fog = f(g(x))

Given: f = {(1, 4), (2, 1), (3, 3), (4, 2)} and g = {(1, 3), (2, 1), (3, 2), (4, 4)}

Solution: We have,

fog(1) = f(g(1)) = f(3) = 3

fog(2) = f(g(2)) = f(1) = 4

fog(3) = f(g(3)) = f(2) = 1

fog(4) = f(g(4)) = f(4) = 2

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

(iii) fof

To find: fof

Formula used: f o f = f(f(x))

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

Solution: We have,

fof(1) = f(f(1)) = f(4) = 2

fof(2) = f(f(2)) = f(1) = 4

fof(3) = f(f(3)) = f(3) = 3

fof(4) = f(f(4)) = f(2) = 1

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