(i) g o f

To find: g o f

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

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

(ii) f o g

To find: f o g

Formula used: f o g = 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

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

(iii) f o f

To find: f o f

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

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