Q. 435.0( 1 Vote )

If the mapping f : {1, 3, 4} {1, 2, 5} and g : {1, 2, 5} {1, 3}, given by

f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3), write fog.

Answer :

Formula:-


(i)Let f : AB and g : BC be two functions.


Then, the composition of f and g, denoted by g o f, is defined as the function g o f : AC


given by g o f (x) = g (f (x))


Given:-


(i)f : {1, 3, 4} {1, 2, 5}


(ii)g : {1, 2, 5} {1, 3}


(iii)f = {(1, 2), (3, 5), (4, 1)}


(iv)g = {(2, 3), (5, 1), (1, 3)


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


fog(2)=f(g(2))=f(3)=5


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


fog={(1,5)(2,5)(5,2)}


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