3. Define sets A = {a,b,c}, B = {x,y}, and C = {1,2,3}. Define the function f :

Question

3. Define sets A = {a,b,c}, B = {x,y}, and C = {1,2,3}. Define the function f : A right arrow B by f = {(a,y),(b,x),(c,x)} and the function g : B right arrow C by {(x,2),(y,1)}. Can the function composition g o f be defined? If so, give the domain, target, and set description of the function. If not, describe why not. 5. Define sets A = {a,b,c}, B = {x,y}, and C = {1,2,3}. Define the function f : A right arrow B by f = {(a,y),(b,x),(c,x)} and the function g : C right arrow B by {(1,y),(2,y),(3,x)}. Can the function composition g o f be defined? If so, give the domain, target, and set description of the function. If not, describe why not.

Explanation / Answer

3) Yes for the first case gof can be defined.

gof = g ( f (x) ) .. which means that for the function to be defined the range of f (x) should be a subset of domain of g (x)

which turns out to be true for the given f(x) and g(x)

4) No ! gof cannot be defined.. As mentioned above the range of f(x) should be a subsetof domain of g(x).. Clearly not true in this case,,,

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