If the function `fa n dg` are given by `f={(1,2),(3,5),(4,1)}a n dg="("(2,3),(5,1),(1,3)"}",` find range of `fa n dg` . Also, write down `foga n dgof` as sets of ordered pairs.

Explanation

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

`:.` Range of `f = {2,5,1}`

`:.` Range of `g = {3,1}`

Now, `fog(2) = f(g(2)) = f(3) = 5`

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

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

`:. fog = {(2,5),(5,2),(1,5)}`


Now, `gof(1) = g(f(1) )= g(2) = 3`

...