Let f : R R : f(x) = x + 1 and g : R R : g(x) = 2x – 3.Find

(i) (f + g) (x)


(ii) (f – g) (x)


(iii) (fg) (x)


(iv)(f/g) (x)


(i) Given:


f(x) = x + 1 and g(x) = 2x -3


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


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


= (x + 1) + (2x -3)


= x + 1 + 2x – 3


= 3x – 2


Therefore,


(f + g) (x) = 3x -2


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


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


= (x + 1) - (2x -3)


= x + 1 - 2x + 3


= 4 - x


Therefore,


(f - g) (x) = 4 - x


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


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


= (x+1) (2x-3)


= x(2x) -3(x) +1(2x) -1(3)


= 2x2 – 3x + 2x -3


= 2x2 – x -3


Therefore,


(fg)(x) = 2x2 – x -3


(iv) To find


Sol.



Therefore,



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