Answer :

(i) Given:


f(x) = 2x + 5 and g(x) = x2 + x


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


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


= (2x + 5) + (x2 + x)


= 2x + 5 + x2 + x


= x2 + 3x + 5


Therefore,


(f + g) (x) = x2 + 3x + 5


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


(f - g) (x) = f(x) - g(x)


= (2x + 5) - (x2 + x)


= 2x + 5 - x2 - x


= -x2 + x + 5


Therefore,


(f + g) (x) = -x2 + x + 5


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


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


= (2x + 5).(x2 + x)


= 2x(x2) + 2x(x) + 5(x2) + 5x


= 2x3 + 2x2 + 5x2 + 5x


= 2x3 + 7x2 + 5x


Therefore,


(fg) (x) = 2x3 + 7x2 + 5x


(iv) To find




Therefore,



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