Question -
Answer -
Given f = {(3, 1), (9,3), (12, 4)} and g = {(1, 3), (3, 3) (4, 9) (5, 9)}
f : {3, 9, 12} → {1, 3, 4} and g : {1, 3, 4, 5} → {3, 9}
Co-domainof f is a subset of the domain of g.
So, gof exists and gof: {3, 9, 12} → {3, 9}
(gof) (3) =g (f (3)) = g (1) = 3
(gof) (9) =g (f (9)) = g (3) = 3
(gof) (12) =g (f (12)) = g (4) = 9
⇒ gof ={(3, 3), (9, 3), (12, 9)}
Co-domainof g is a subset of the domain of f.
So, fog exists and fog: {1, 3, 4, 5} → {3, 9, 12}
(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
⇒ fog ={(1, 1), (3, 1), (4, 3), (5, 3)}