Let f : {3, 9, 12} → {1, 3, 4} and g : {1, 3, 4, 5} → {3, 9} be
defined 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).
(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
Ans) 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
Ans) f o g = {(1, 1), (3, 1), (4, 3), (5, 3)}