. Let f: R → R: f(x) = x3 + 1 and g: R → R: g(x) = (x + 1). Find:
(i) (f + g) (x)
(ii) (f – g) (x)
(iii) (1/f) (x)
(iv) (f/g) (x)
(i) Given:
f(x) = x3 + 1 and g(x) = x + 1
(i) To find: (f + g) (x)
(f + g) (x) = f(x) + g(x)
= (x3 + 1) + (x + 1)
= x3 + 1 + x + 1
= x3 + x + 2
Therefore,
(f + g) (x) = x3 + x + 2
(ii) To find: (f - g) (x)
(f - g) (x) = f(x) - g(x)
= (x3 + 1) – (x + 1)
= x3 + 1 – x - 1
= x3 - x
Therefore,
(f - g) (x) = x3 - x
(iii) To find
Therefore,
(iv) To find
(Because a3 + b3 = (a + b) (a2 – ab + b2))
Therefore,
= x2 – x + 1
1