Answer :

Given:


f(x)=: x > 2 and g(x)= :x > 2


(i) To find: (f + g) (x)


Domain(f) = (2, ∞)


Range(f) = (0, ∞)


Domain(g) = (2, ∞)


Range(g) = (2, ∞)


(f + g) (x) = f(x) + g(x)


=


Therefore,


(f + g) (x) =


(ii) To find:(f - g)(x)


Range(g) Domain(f)


Therefore,


(f - g)(x) exists.


(f - g)(x) = f(x) – g(x)


=


Therefore,


(f - g) (x) =


(iii) To find:(fg)(x)


(fg)(x) = f(x).g(x)


=


=


=


=


Therefore,


(fg)(x) =


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