Find (f/g)(x) for f(x) = 1/x and g(x) = x^3. Show work and state the domain of (f/g)(x)

(f/g)(x) = f(x)/g(x) = (1/x)/(x^3) = 1/x^4

clearly the domain of f/g is all reals except 0, as are the domains of f and g separately.

Note, however, that (fg)(x) = x^2, whose domain is all reals, but since f and g are not defined at x=0, neither can (fg) be.