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) }`
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)}`