Let f : {3, 9, 12} → {1, 3, 4} and g : {1, 3, 4, 5}→ {3, 9} bedefi

1.	Let f : {3, 9, 12} → {1, 3, 4} and g : {1, 3, 4, 5}→ {3, 9} bedefined as f = {(3, 1), (9, 3), (12, 4)} and g = {(1, 3), (3, 3), (4, 9), (5, 9)}. Find (i) (g o f) (ii) (f o g).
Answer» (i) g o f To find: g o f Formula used: g o f = g(f(x)) Given: f = {(3, 1), (9, 3), (12, 4)} and g = {(1, 3), (3, 3),(4, 9), (5, 9)} Solution: We have, gof(3) = g(f(3)) = g(1) = 3 gof(9) = g(f(9)) = g(3) = 3 gof(12) = g(f(12)) = g(4) = 9 g o f = {(3, 3), (9, 3), (12, 9)} (ii) f o g To find: f o g Formula used: f o g = f(g(x)) Given: f = {(3, 1), (9, 3), (12, 4)} and g = {(1, 3), (3, 3),(4, 9), (5, 9)} Solution: We have, fog(1) = f(g(1)) = f(3) = 1 fog(3) = f(g(3)) = f(3) = 1 fog(4) = f(g(4)) = f(9) = 3 fog(5) = f(g(5)) = f(9) = 3 f o g = {(1, 1), (3, 1), (4, 3), (5, 3)}

Let f : {3, 9, 12} → {1, 3, 4} and g : {1, 3, 4, 5}→ {3, 9} bedefined as f = {(3, 1), (9, 3), (12, 4)} and g = {(1, 3), (3, 3), (4, 9), (5, 9)}. Find (i) (g o f) (ii) (f o g).

Answer»

(i) g o f

To find: g o f

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

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

Solution: We have,

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

gof(9) = g(f(9)) = g(3) = 3

gof(12) = g(f(12)) = g(4) = 9

g o f = {(3, 3), (9, 3), (12, 9)}

(ii) f o g

To find: f o g

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

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

Solution: We have,

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

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

fog(4) = f(g(4)) = f(9) = 3

fog(5) = f(g(5)) = f(9) = 3

f o g = {(1, 1), (3, 1), (4, 3), (5, 3)}