If the functions `f` and `g` are given by `f={(1,\ 2),\ (3,\ 5),\ (4,\ 1)}` and `g={(2,\ 3),\ (5,\ 1),\ (1,\ 3)}` , find range of `f` and `g` . Also, write down `fog` and `gof` as sets of ordered pairs.

Answer

N/a

Explanation

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