. Let f: R → R: f(x) = x^{3} + 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) = x^{3} + 1 and g(x) = x + 1

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

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

= (x^{3} + 1) + (x + 1)

= x^{3} + 1 + x + 1

= x^{3} + x + 2

Therefore,

(f + g) (x) = x^{3} + x + 2

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

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

= (x^{3} + 1) – (x + 1)

= x^{3} + 1 – x - 1

= x^{3} - x

Therefore,

(f - g) (x) = x^{3} - x

(iii) To find

Therefore,

(iv) To find

(Because a^{3} + b^{3} = (a + b) (a^{2} – ab + b^{2}))

Therefore,

= x^{2} – x + 1

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