Answer
$(f \circ g)(x) = x^4$,
$(g \circ f)(x) = x^4$.
Domains: $(-\infty, 0) \cup (0, \infty)$.
Work Step by Step
$(f \circ g)(x) = f(g(x)) = f(x^{-4}) = (x^{-4})^{-1} = x^4$,
$(g \circ f)(x) = g(f(x)) = g(x^{-1}) = (x^{-1})^{-4} = x^4$.
The domains $D_f, D_g$ are the same and equal to $(-\infty, 0) \cup (0, \infty)$.
Similarly, the domains of the compositions $f \circ g$ and $g \circ f$ are the same and equal to $(-\infty, 0) \cup (0, \infty)$.
