Seeing as this is posted under function composition, I'll treat
(f * g)(x) as the composition f(g(x)).
The domain of f is RR, since any real x can be squared.
The domain of g is [0, +infty) because roots only accept non negative input.
The composition is defined, when x is in the domain of g, and g(x) is in the domain of f. In other words:
With f(g(x)), x is the input (independent variable) for g, and g(x) is the input for f. Therefore, the inputs each must be part of the domains of the functions they are to be used in. We have the following constraints:
x must be non-negative, since it goes into the function g(x) = sqrtx.
g(x) must be real (it obviously is).
Therefore,
f(g(x)) = (sqrtx)^2 = x, for x >= 0.
