Given and g(x) = x

Domain of f = [0, ∞)

Domain of g = R

i. f + g

We know (f + g)(x) = f(x) + g(x)

Domain of f + g = Domain of f ∩ Domain of g

⇒ Domain of f + g = [0, ∞) ∩ R

∴ Domain of f + g = [0, ∞)

Thus, f + g : [0, ∞) → R is given by

ii. f – g

We know (f – g)(x) = f(x) – g(x)

Domain of f – g = Domain of f ∩ Domain of g

⇒ Domain of f – g = [0, ∞) ∩ R

∴ Domain of f – g = [0, ∞)

Thus, f – g : [0, ∞) → R is given by

iii. fg

We know (fg)(x) = f(x)g(x)

Clearly, (fg)(x) is also defined only for non-negative real numbers x as square of a real number is never negative.

Thus, fg : [0, ∞) → R is given by

iv.

We know

Clearly, is defined for all positive real values of x, except for the case when x = 0.

When x = 0, will be undefined as the division result will be indeterminate.

⇒ Domain of = [0, ∞) – {0}

∴ Domain of = (0, ∞)

Thus, : (0, ∞) → R is given by