Given functions $f$ and $g$, find $(a)(f \circ g)(x)$ and its domain, and $(b)(g \circ f)(x)$ and its domain. \[ f(x)=x^{3}, g(x)=x^{2}+2 x-4 \]

Step 1 ：Given functions \(f(x)=x^{3}\) and \(g(x)=x^{2}+2 x-4\)

Step 2 ：For \((f \circ g)(x)\), we substitute \(g(x)\) into \(f(x)\), we get \((f \circ g)(x) = (x^{2}+2x-4)^{3}\)

Step 3 ：The domain of \((f \circ g)(x)\) is all real numbers

Step 4 ：For \((g \circ f)(x)\), we substitute \(f(x)\) into \(g(x)\), we get \((g \circ f)(x) = (x^{3})^{2}+2(x^{3})-4 = x^{6}+2x^{3}-4\)

Step 5 ：The domain of \((g \circ f)(x)\) is all real numbers

Step 6 ：Final Answer: \(\boxed{(a) (f \circ g)(x) = (x^{2}+2x-4)^{3}}\), its domain is all real numbers

Step 7 ：Final Answer: \(\boxed{(b) (g \circ f)(x) = x^{6}+2x^{3}-4}\), its domain is all real numbers