Let f = {(1, 2), (3, 5), (4, 1) and g = {(2, 3), (5, 1), (1, 3)}. Then g o f = ______and f o g = ______.

Question

Fill in the blanks:

Let f = {(1, 2), (3, 5), (4, 1) and g = {(2, 3), (5, 1), (1, 3)}. Then g o f = ______and f o g = ______.

Answer 1

Given that,

f = {(1, 2), (3, 5), (4, 1) and g = {(2, 3), (5, 1), (1, 3)}

Now,

gof (1) = g(f(1)) = g(2) = 3

gof (3) = g(f(3)) = g(5) = 1

gof (4) = g(f(4)) = g(1) = 3

∴ gof = {(1,3),(3,1),(4,3)}

fog (2) = f(g(2)) = f(3) = 5

fog (5) = f(g(5)) = f(1) = 2

fog (1) = f(g(1)) = f(3) = 5

∴ fog = {(2,5),(5,2),(1,5)}