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.

Explanation

The range `( f ) = { 1 , 2 , 5 )` and dom `( g ) = { 1 , 2 , 5 }(f)={1,2,5)` and dom `(g)={1,2,5}`

Clearly range `( f ) \subseteq ` dom `( g ) (f)\subseteq dom (g)`

Therefore`(gof)` is defined and
Dom`(gof)=`dom`(f)={1,3,4}.`

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`

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