Let `f={(3,1),(9,3),(12 ,4)}` and `g={(1,3),(3,3),(4,9),(5,9)}dot` Show that `gofa n dfog` are both defined. Also, find `foga n dgofdot`

Explanation

`f={(3,1),(9,3),(12,4)} text { and } g={(1,3),(3,3)(4,9)(5,9)}`



`f:{3,9,12} ->{1,3,4}` and `g:{1,3,4,5} ->{3,9}`


Co-domain of `f` is a subset of the domain of `g`.


So, gof exists and gof : `{3,9,12}->{3,9}`


`(g circ f)(3)=g(f(3))=g(1)=3`


`(g circ f)(9)=g(f(9))=g(3)=3`


`(g circ f)(12)=g(f(12))=g(4)=9`


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