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 orderedpairs.

If the functions `f`and `g`are given by `f={(1, 2), (3, 5), (4, 1)}`an

1.	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 orderedpairs.
Answer» Here range `(f) ={1,2,5) " and dom " (g) ={1,2,5}` Clearly range `(f ) sube " dom " (g)` `:. (g o f)` is defined and dom `( g o f) = " dom " (f ) = {1,3,4}` Now `(g o f) (1) = g { f (1) } =g (2) =3:` `(g o f) (4) =g { f (4) } +g (1) =3` Hence (g o f) `= {(1,3),(3 ,1) (4,3)}` Again range (g) `={1,3}` and dom (f ) ={1,3,4} Clearly rangle (g) ` sube` dom (f ) `:. ` (f o g ) is defined and dom (f o g) = dom (g) = {1,2,5} Now (f o g) (1) `= f {g (1)} =f (3) =5,` ` (f o g) (2) = f { g (2)} =f (3) =5,` `(f o g) (5) =f { g (5) } =f (1) =2` Hence (f o g) ={(1,5) ,(2,5) ,(5,2)}