. Let f:(2, ∞) → R: f(x) = and g: (2, ∞) → R: g(x) = Find: (i) (f + g) (x) (ii) (f - g) (x) (iii) (fg) (x)

Question

Philoid · Accepted Answer

Given:

f(x)=: x > 2 and g(x)= :x > 2

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

Domain(f) = (2, ∞)

Range(f) = (0, ∞)

Domain(g) = (2, ∞)

Range(g) = (2, ∞)

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

=

Therefore,

(f + g) (x) =

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

Range(g) Domain(f)

Therefore,

(f - g)(x) exists.

(f - g)(x) = f(x) – g(x)

=

Therefore,

(f - g) (x) =

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

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

=

Therefore,

(fg)(x) =