. 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)

Question

Philoid · Accepted Answer

(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

. 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)