माना कि A = {1,2,3,4,5}. माना कि `f : A rarr A` तथा इस प्रकार परिभाषित है कि, f(1) = 2, f(2) = 3, f(3) = 4, f(4) = 5, f(5) = 1 तथा g(1) = 4, g(2) = 1. g(3) = 1, g(4) = 2, g(5) = 3. फलन fog तथा gof निकालें ।

Explanation

प्रश्न से, f(1) = 2, f(2) = 3, f(3) = 4, f(4) = 5, f(5) = 1
g(1) == 4, g(2) = 1, g(3) = 1, g(4) = 2, g(5) = 3
(fog)(1) = f(g(1)) = f(4) = 5
(fog)(2) = f(g(2)) = f(1) = 2
(fog)(3) = f(g(3)) = f(1) = 2
(fog)(4) = f(g(4)) = f(2) = 3
तथा (fog)(5) = f(g(5)) = f(3) = 4
अतः फलन fog = {(1, 5), (2,2), (3,2), (4,3), (5,4)}
पुनः (gof)(1) = g(f(1)) = g(2) = 1
(gof)(2) = g(f(2)) = g(3) = 1
(gof)(3) = g(f(3)) = g(4) = 2
(gof)(4) = g(f(4)) = g(5) = 3
तथा (gof)(5) = g(f(5)) = g(1) = 4
अतः फलन gof = {(1,1), (2, 1), (3, 2), (4, 3), (5, 4)}