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