माना कि `A = {1, 2, 3, 4}`, `f =` {(1, 4), (2, 1), (3, 3), (4, 2)} तथा `g =` {(1, 3), (2, 1), (3, 2), (4, 4)}
ज्ञात करे (i) fog, (ii), gof, (iii) fof

Explanation

दिया है, A = {1,2,3,4}
f = {(1,4), (2,1), (3,3), (4,2)}
g = {(1,3), (2, 1), (3, 2), (4, 4)}
f का प्रान्त = {1,2,3,4}
f का परिसर = {4,1,3,2}, g = {1,2,3,4}
g का प्रान्त = {1,2,3,4}, g का परिसर = {3,1,2,4} = {1,2,3,4}
स्पष्टतः f का प्रान्त g = का परिसर
तथा g का प्रान्त = f का परिसर
अतः fog तथा gof परिभाषित हैं।
साथ ही यहाँ fof भी परिभाषित है।
(i) (fog) (1) = f(g(1)) = f(3) = 3
(fog)(2) = f(g(2)) = f(1) = 4
(fog)(4) = f(g(4)) = f(4) = 2
अतः fog = {(1,3), (2, 4), (3,1), (4, 2)}
(ii) (gof)(1) = g(f(1)) = g(4) = 4
(gof)(3) = g(f(3)) = g(3) = 3
(gof)(4) = g(f(4)) = g(2) = 1
अतः gof = {(1, 4), (2, 3), (3, 2), (4, 1)}
(iii) (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
अतः fof = {(1, 2), (2, 4), (3, 3), (4, 1)}