Find the natural domain of the function?

Question

g(u) = (sqaure root)u - (square root) (7 - u)

Answer 1

The function is g(u) = √u - √(7-u).

For the function g = f - h, the domains are defined as the inrersection of the domains of f and h.

The domain of f(u) = √u is [0, +∞).

The domain of h(u) = √(7-u) ≥ 0 ⇒ 7 ≥ u  ⇒ (0, 7].

The domain of g(u) = √u is (0, 7] ∩ [0, +∞) = [0, 7].