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)

= 2x^{2} – 3x + 2x -3

= 2x^{2} – x -3

Therefore,

(fg)(x) = 2x^{2} – x -3

(iv) To find

Sol.

Therefore,

1